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LIBRARY OF CONGRESS, 



Cha^2Q.aitopyright No... 
SheiaQSJ. 



UNITED STATES OF AMERICA. 



PHYSICAL 



Laboratory Manual 



AND NOTE-BOOK 



BY 



J. B. GREGG, A. M. 

INSTRUCTOR IN PHYSICS, OHIO NORMAL 
UNIVERSITY. 







ADA, OHIO: 

The University Herald Press, 

189 8. 

• ; 

■ TWO COPIES RECEIVED 

~17 



c 



2919 



COPYRIGHT, 1898, 



The Author. 



T^7E are indebted to the kindness of the 
W. A. Olmsted Scientific Company, 
Chicago, for furnishing the illustrations 
that were not made specially for this 
work. 



CONTENTS. 



TO THE STUDENT. 

PAGE 

Directions for Laboratory Work . 1 

Tabulated Reports and References 2 

Discussion of Experiments 3 

Curves 4 

MECHANICS. 
Measurements. — 

Of Length 8 

Of Mass and Volume 10 

Motion — 

Inertia 12 

Curvilinear Motion ......... 14 

Parallelogram of Forces . . . . . .16 

Forces of Nature. — 

1. Gravity. 

Laws of Accelerated Motion 18 

Gravity by Atwood's Machine .... 20 

Laws of the Pendulum 22 

Gravity by the Simple Pendulum .... 24 

2. In Liquids. 

Cohesion, Adhesion, Capillarity .... 26 

Specific Gravity 28 

3. In Gases. 

Boyle's Law . .30 

The Air Pump 32 

The Siphon - .34 



vi CONTENTS. 

Energy. — 

Pulleys, Wheel and Axle 36 

HEAT. 

Laws of Boiling- 38 

To Correct a Thermometer 40 

Radiation 42 

Water Equivalent of a Vessel ........ 44 

Specific Heat 46 

Latent Heat of Fusion 48 

Latent Heat of Vaporization 50 

Coefficient of Expansion of Gases . . . . . . .52 

Linear Expansion or Solids 54 

SOUND. 

Theory of Sound 56 

Laws of Vibrating- Strings ........ 58 

Characteristic Properties of Musical Sound 60 

Velocity of Sound . . . . . . . . . .62 

Interference ............ 64 

EIGHT. 



Intensity and Absorption 
Reflection and Refraction 
Focal Lengths 
Production of Colors 
Classification of Colors 
Spectra .... 



66 

68 
70 

72 
74 
76 



MAGNETISM AND ELECTRICITY. 

Magnetism. — 

Lines of Force and Magnetic Field 78 

Induction 80 

Laws of Magnetic Force ....... 82 

Static Electricity. — 

Electrostatic Induction 84 

Condensers 86 

The Holtz Machine 88 

Effects of the Discharge 90 



CONTENTS. vii 

The Electric Current — 

Effects of Current . .92 

Tangent Galvanometer . . . . . . .- .94 

Calibration of a Galvanometer ...... 96 

Law of Shunts 98 

Arrangement of Cells ........ 100 

Electromotive Force. — 

Electromotive Force of Cells 102 

Fall of Potential Over a Wire 104 

Polarization 106 

Resistance. — 

Substitution 108 

Resistance in Parallel Circuit 110 

Specific Resistance. 112 

Temperature Coefficient 114 

Induction 116 

The Dynamo 118 

Questions 120-137 

Problems .-...• 138 

Tables 153 



PHYSICAL LABORATORY 

MANUAL AND NOTE-BOOK. 



TO THE STUDENT. 

The work in the laboratory is intended: — 

(i.) To impress upon the mind the principles and laws 
that have been taught by text-books. 

(2.) To cultivate proper methods of observation. 

(3.) To acquaint the student with physical apparatus and 
physical experimentation. 

(4.) To develop the understanding. 

Bear in mind: — 

(1.) That a collection of facts is not an education. 

(2.) That the understanding is to be used as well as the 
memory. 

(3.) That the object of an education is to develop the 
power to think more accurately, feel more deeply, act more 
nobly. 

Make it an established custom: — 

(1.) To attempt nothing without preparing as thoroughly 
as possible beforehand. 

(2.) To be exact and work methodically. 
(3.) To use your own eyes, and to do your own thinking. 
(4.) To give your constant attention to your own work. 
(5.) To record observations at the time they are made. 



2 PH YSICA L LAB OR A TOR Y MANUAL. 

(6.) To rely on yourself, and not to expect the instructor 
to make the experiment for you. 

(7.) To discuss the work orally with those who experiment 
with you. 

(8.) To clean the apparatus, and place them where they 
belong. 

THE REPORT, 

\+ Tabulated Report and References* 

In all experiments in which there are data to be obtained, the 
data should be tabulated. The following is a tabulated report 
of Exp. 47: — 



R, 


R« 


R c 


R s 


R 2s 


R, 


c, 

.35 
.34 

.32 


c 2s 


c, 


References 


0. 

.5 
2. 








.7 
.6 
.5 


2.2 
1.2 

.4 


Au. 


p. 


§ 












A. 


139 


(135 
(136 


4. 












.28 


.35 


.22 






8. 


.001 


3. 


18. 


4.5 


.5 


.24 


.25 


.12 


Cu 


189 ! i 


10. 












.22 


.22 


.1 




I 119 


12. 












.2 


.18 


.09 


U. 


219 13 


15. 












.18 


.15 


.07 


Poy. 


178 


18. 












.16 


.12 


.05 




1 



Minotto's cells were used. A Minotto cell is formed by placing 
the following" layers, in the order named, in a glass jar: a copper 
plate attached to an insulated copper wire, crystals of copper sulphate, 
thin canvas, sawdust, thin canvas, zinc plate. The cell is completed 
by pouring in a solution of zinc sulphate. The internal resistance 
may be regulated by the thickness of the layer of sawdust, by acid- 
ulating with sulphuric acid, or by adding common salt. It will re- 
quire some time for the solution to soak through the layer of sawdust. 

The student will tabulate neatly the data of each experi- 
ment, at the top of the page opposite the directions for mak- 
ing the experiment. 

The references the student has made in preparing the dis- 
cussion should be tabulated as shown above. The report 
should show the author, the page, and the section that has 



THE REPORT. 3 

been read. The following is a partial list of the works that 
the student will find serviceable in preparing for the discus- 
sions. The letters given are to be used in the report to des- 
ignate the author: 

A., Ayrton's Practical Electricity. 

B., Barker's Physics. 

C., Carhart's University Physics. 

C. and P., Carhart and Patterson's Electrical Measurements . 

Cu., Cumming's Electricity. 

F., Faraday's Experimental Researches. 

G., Gray's Absohite Measurements in Electricity. 

Ga., Ganot's Physics — Translated by Atkinson. 

GL, Glazebrook's Physical Optics. 

Gr., Gross' Elementary Dynamics. 

H., Helmholtz's On the Sensation of Tone. 

L., Lodge's Elementary Mechanics. 

Lo., Lommel's The Nature of Light. 

La., Lardon's Electricity. 

LI., Lloyd's Magnetism. 

Mad., Madan's^^ Elementary Text- Book on Heat. 

Max., Maxwell's Matter and Motion. 

N., Nichol's Laboratory Manual of Physics and Applied Elec- 
tricity. 

P., Preston's Theory of Light. 

Poy., Poyser's Magnetism and Electricity. 

Sp., S prague's Electricity. 

St., Stewart's Elementary Physics. 

S. and G., Shaw and Glazebrook's Practical Physics. 

T., Tait's Light. 

Th., Thompson's Dynamo-Electric Machinery. 

Tyn., Tyndall's Sound. 

W., Wright's Heat. 

2* Discussion. 

The questions given to aid in the discussion are intended: — 
(i.) To suggest what may be learned from the experiment. 



4 PH YSICAL LABOR A TOR Y MANUAL. 

(2.) To suggest other experiments that will aid in giving a 
better understanding of the principles involved. 

(3.) To suggest the method to be followed in developing 
some fact, principle, or law. 

In the space below the tabulated data write, in as nearly a 
connected manner as possible, the discussion. It should not 
have the appearance of answers to test questions of an exam- 
ination. Use the questions until a thorough understanding of 
the principles is obtained. In writing the discussion, the less 
attention given to the questions, and the more attention given 
to the principles involved, the better the discussion will be. 

3* Curves* 

The Graphic Method of representing the result of an ex- 
periment is often better than any other way of demonstrating 
the truths taught by the experiment. The curves, page 5, 
are formed from the tabulated data given on page 2. 

The point (0,0) is the origin. The horizontal line through 
the origin is the axis of abscissas. The vertical line through 
the origin is the axis of ordinate s. The cross lines are to aid 
in locating the points. 

It is not often necessary to give the spaces between the hori- 
zontal lines the same value as is given the spaces between the 
vertical lines. It is often more convenient to give them dif- 
ferent values. If there be no reason for having them repre- 
sent the same value, the value given to the space between 
horizontal lines, and that given to the space between vertical 
lines should be determined respectively from the greatest 
values of the ordinates and abscissas. Choose the smallest 
convenient value for the distance between vertical lines, that 
will keep the abscissa of greatest value on the horizontal axis. 
Choose that value for the distance between horizontal lines, 
that will be most convenient in drawing the curve. 

To fix the scale from the data in the table, look for the 
abscissa of greatest value. It is in the column R h . The great- 



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6 PHYSICAL LABORATORY MANUAL. 

est one is 18. The smallest convenient value that can be 
given to the space between vertical lines is 1.5. As a con- 
venient value for the space between horizontal lines .4 is 
taken. 

To plot the points for the curve C p , the resistances in the 
column R,, are used as abscissas, and the corresponding cur- 
rents in the column C p , as ordinates. The first pair of values 
is (0,2.2). The coordinates (0,2.2) mean that the point is at 
the intersection of the vertical line representing no resistance, 
with the horizontal line representing 2.2 amperes current. 
It is the highest point marked on the curve C p . The next co- 
ordinates are (.5,1.2). The point is at the intersection of the 
vertical line representing .5 ohm resistance with the hori- 
zontal line representing 1.2 ampere current. These lines are 
not drawn in the figure, but they can be located easily by 
means of the cross lines. The point is the second one on the 
curve C p , marked by a small circle. All the different points 
for C p , given by the data, are thus plotted. 

To draw the curve C p , connect the points plotted, by a 
smooth curve. Since the data will contain some errors, a 
smooth curve will not pass through all the points. The curve 
shows the mean direction of the plotted points. The values 
taken from points on the curve will be more trustworthy than 
the data obtained by experiment. 

4* Problems* 

Place the solution for each problem on the blank page op- 
posite the problem solved. Indicate the operations. 

N. B. Full credit will not be given, unless a sufficient number of 
trials have been made to insure accuracy, and the reports have been 
neatly and carefully written. 



TABULATED RESULTS. 

Before attempting an experiment, read carefully the ques- 
tions intended to aid in the discussion. A neglect of this 
may make it necessary to perform the experiment again. 

Do not rely on one observation, but take the average of 
several values found by experiment. Tabulate the results of 
each trial as in the following table for Exp. No. i: — 



T 


L 


D w 


T 


1 


R 


R s 


r 


•L'jre 


w 


D, 




c m 


m m 


m m 


m m 


m m 


m m 


m. m 


c m 


g 


tn m 


l 


22.21 


4.41 


2.14 


75 


.03 


4 14 




18.5 


12.5 




2 


22.18 


4 45 


2.14 


76 


.03 


4.12 




18.45 


12.5 




3 


22.23 


4.43 


2.16 


78 


.02 


4.12 




18.45 


12.52 




4 


22.21 


4.44 


2.15 


76 


.02 


4.12 




18.5 


12.52 




Avg" 


22.21 


4 43 


2.15 


76 


.025 


4.125 


237.5 


18.48 


12.51 


.8 



T represents the different trials. 



MECHANICS. 



EXPERIMENT i. 

MEASUREMENTS OF LENGTHS. 





Micrometer Caliper. 



Method*— i. Measure the 
length of a bar with the ver- 
niered caliper. 

2. Measure the diameter 
of a wire with the micrometer 
caliper. 

3. Measure the 
thickness of a plate 
of glass with the 
spherometer. 

4. Measure the 
radius of a sphere 
with the spherom- 
eter. 

5. Measure the 
inside diameter of 



a small glass tube. 

Clean the tube by washing with hy- 
drochloric acid, water, and then with 
alcohol. Partly fill the tube with mer- 
cury, and lay it on a horizontal sur- 
face. Measure the length of the col- 
umn of mercury as in 1. Since a cu- 
bic centimeter of mercury weighs 13.6 
g., the diameter can be found from the 
length and weight of a column of 
mercury. 

Data.— 1. L, length of the bar. 2. 
D VJ , diameter of the wire. 3. Tg , the 
thickness of the glass. 4. (1.) /, the 
length of one side of the triangle 
formed by the three fixed points of the 
spherometer; (2.) R, the reading when 
the four points rest on a smooth surface; (3.) R s , the reading on the 
sphere; (4.) r, the radius of the sphere. 5. (1.) L m , length of the mer- 
cury column; (2.) IV, weight of mercury; (3.) D t , diameter of tube. 




Spherometer. 



I- 4- 6(R—R) + 



h(R, 



-R) 



10 



MEASUREMENTS. 




Beam Balance. 



EXPERIMENT 2. 

VOLUME AND MASS. 

Method. — I. Find the vol- 
ume of an irregular body. 

Partly fill a graduated cylin- 
der with water, and immerse 
the irregular body in it. The 
volume is the difference in the 
volumes shown by the water be- 
fore and after immersion. 

2. Find the volume of a 
piece of glass tubing. 

3. Find the volume of a 
cylindrical jar. 

4. Find the mass of an object with the beam balance. 

5. Find the mass of an object with the Jolly balance. (Fig., 
Exp. 11.) 

Data.— 1. (1.) V w , the volume of water; (2.) V ts the tot?! 
volume of water and irregular body; (3.) V it the volume of 
the irregular body. 

2. (1.) D h , the diameter of bore — found as in 5, Exp. 1; 
(2.) D , outside diameter — found as in 2, Exp. 1; (3.) L ti the 
length of the tube — found as in 1, Exp. 1; (4.) V t , the vol- 
ume of the tubing. 

3. (1.) L r , the length of a vertical rod from the surface of 
the water filling the cylinder to the bottom of the cylinder; 
(2.) D;, the inside diameter of the cylinder — found by open- 
ing the caliper within the cylinder, the two points at the level 
of the water partly filling the cylinder; (3.) V c , the volume 
of the cylinder. 

4. M, the mass that produces a balance. 

5. M e , the mass that produces an equal elongation. 



12 



MOTION. 



EXPERIMENT 3. 

ROTATOR, INERTIA. 





Rotator. 



Inertia Apparatus. 



I. Any convenient form of rotator 
may be used. The one shown in the cut 
will serve many purposes in the labora- 
tory. Very good results can be ob- 
tained by rotating by means of a string 
and the fingers. 

The objects rotated should include the 
following: an endless chain, a hoop, and oblate spheroid so 
arranged that it can be suspended from different points, a 
prolate spheroid arranged in the same manner, a cylinder, 
two balls of unequal mass fastened together by a rod 8 or 10 
inches long, and a glass globe partly filled with water. 

2. (1.) Use the inertia apparatus. (2.) Lay a coin on a 
smooth card supported by the end of the finger. Fillip the 
card from the finger by striking it squarely on the edge. 

Pull the card from the finger. Do not jerk it. 

Data. — 1. (1.) 0, the object rotated; (2.) 5, the point of 
suspension; (3.) A, the axis of rotation. 



14 



MO TION. 



EXPERIMENT 4. 

CURVILINEAR MOTION. 




Centrifugal Force Apparatus. 

The following laws are to be tested: 

1. The centrifugal force varies directly as the mass when the 
radius and the velocity are constant. 

2. The centrifugal force varies directly as the square of the 
velocity when the mass and radius are constant. 

3. The centrifugal force varies inversely as the radius when 
the mass and velocity are constant. 

Method. — Rotate the apparatus shown in the figure, by 
means of the rotator used in Exp. 3. 

Data. — ( 1. ) My the mass rotating; (2.) R, the corresponding 
radius of rotation; (3.) N, the number of rotations per sec. as 
shown by a speed indicator; (4.) W, the weight lifted. 

Test each law by using three or four values for the variable. Any 
two values of the variable and the corresponding- weights lifted should 
give the proportion expressed in the law. 

The radius of rotation should be measured to the center of the ro- 
tating mass. 



16 



MOTION. 



EXPERIMENT 5. 



PARALLELOGRAM OF FORCES. 



Method. — I. Arrange two weights by means of the pulleys, 
at any desired angle. Fasten the cords at the center of the 

board. From the point of 
intersection of the cords, 
plot off along each cord a 
distance in inches equal to 
the force in pounds acting 
on the cord. Complete the 
parallelogram, and find the 
resultant. Now place a third 
pulley and weight so that 
the three cords, fastened to- 
gether and free to move, 
will intersect at the center. 

2. Proceed as in 1 to find 
the resultant when three 
pulleys and weights are 

Apparatus for the Parallelogram USecl. 

of Forces. 

Data.— (1) W u the weight 
used for the first force; (2.) W 2 , the weight used for the sec- 
ond force; (3.) W^, the weight used for the third force; (4.) 
W r , the weight showing the resultant of the forces; (5.) L r , 
the length in inches of the resultant shown by the parallelo- 
gram; (6.) E d , the error in the direction of the resultant 
(7.) E r , the error in the resultant. 

E d is the angle formed by the intersection of the line repre- 
senting the resultant and the cord supporting the resultant 
weight. 

L r — W r = E r . 




18 



FORCES OF NA TURE.—GRA VITY. 



EXPERIMENT 6. 



LAWS OF UNIFORMLY ACCELERATED MOTION. 




Method* — Place equal weights on the 
ends of the cord of Atvvood's Machine. 
Then add small pieces of cardboard to 
the weight that is to carry the rider un- 
til it will continue to move downward 
with a uniform velocity when once 
started. The added weight will not 
produce motion from a state of rest. 
Now place a light rider in position, and 
adjust the ring until it will remove the 
rider after a fall of exactly three sec- 
onds; then four seconds. Adjust the 
table until the weight strikes it in some 
exact number of seconds. 

2. Place a 325 g. weight, including a 
50 g. rider, in position. Make the op- 
posite weight 312.5 g. Adjust the ring 
until the rider will be removed at the 
end of the second second; then at the 
end of the third second; and, lastly, 
the fourth second. 

Data.— 1. (1.) T r , the time until the 
rider is removed; (2.) T w , the time 
until the weight strikes the table; (3.) 
S t , , the corresponding space traversed 
with the uniform velocity; (4.) A, the 
acceleration. 

2. (1.) /, the time until the rider is 
removed; (2.) S a , the corresponding 
space traversed with the accelerated 
velocity; (3.) W u W 2 , the weights. 

Sh is the space between the ring- and the 
table minus the length of the cylindrical 
weight. S a is the space between the drop 
table and the ring- plus the length of the 
cylindrical weight. 



Atwood's Machine. 



s u 



(/;. _ T r ) = A. 



20 FORCES OF NA TURE.—GRA VITY. 



EXPERIMENT 



/ 



DETERMINATION OF GRAVITY BY THE USE OF ATWOOD S 

MACHINE. 

From the data of Exp. 6, we may form the following equa- 
tion : 

( Wi + m + M P )A = ( JF, - W 2 )g 

M p is an unknown resistance due to the inertia of the pul- 
ley; g is gravity. The problem is to find what mass would 
possess the same inertia as is overcome in the pulley, or the 
equivalent mass of the pulley. 

Method* — With all the weights and the heavy rider in posi- 
tion, adjust the ring for a fall of two seconds; then for three 
seconds; and, lastly, four seconds. Perform the same when 
equal small weights are removed from each side; then with 
two weights removed from each side. 

Data. — (i.) M r , the total mass of the weights on the side 
carrying the rider; (2.) M, the mass of the opposite weights; 
(3.) T, the time until the rider is removed; (4.) S, the corres- 
ponding space traversed; (5.) A Cf the calculated acceleration; 
(6.) M p1 the equivalent mass of the pulley; (7) g, gravity. 

The equivalent mass of the pulley remains constant, and can be 
found from the following- proportion: 

m -\- x : ;//' + x :: a' : a. 

m andiwz' = M r -\- M for two different determinations of the accel- 
eration; a and a' are the respective accelerations. 

Mp is the average of the values of x in the three proportions formed 
from the values of 1ST, and /!/. 

g is computed from the first equation given at the top of the page. 

A, is the average for the three trials with the same weights. 



22 



THE FORCES OF NATURE.— GRAVITY. 



EXPERIMENT 8. 



THE LAWS OF THE PENDULUM. 

The following laws of the pendulum are to be tested: 

I. The time of vibration varies as the square root of the length 
when gravity is constant. 

2. The time of vibration is independent of 
the mass of the bob. 

3. The time of vibration is independent of 
the amplitude when it does not exceed abont 
three degrees. 

Method* — 1. Vibrate a pendulum one 
meter in length; then, one .25 meters; 
and so on, changing its length in each 
trial. 

2. Vibrate pendulums of equal lengths 
but of unequal masses. 

3. Vibrate a pendulum through differ- 
ent small arcs. 

Data* — (1.) L, the length of the pen- 
dulum; (2.) M, the mass of the bob; 
(3.) A, the length of the arc; (4.) N, the 
number of vibrations counted; (5.) T, the time of the total 
number of vibrations; (6.) V, the number of vibrations per 
sec; (7.) P, the period of one vibration. 

Tabulate M by stating- whether the masses are alike or different. 
Tabulate A in the same manner. 




Pendulum 
Apparatus 



24 THE FORCES OF NA TURE.—GRA VITY. 



EXPERIMENT 9. 

GRAVITY BY THE SIMPLE PENDULUM. THE PHYSICAL 

PENDULUM. 

Method* — 1. Gravity. Suspend a heavy ball by a fine wire 
or thread; set it vibrating through a small arc; and determine 
the time of one vibration by counting the vibrations for four 
or five minutes. Measure accurately the length of the wire, 
and add to its length one-half the diameter of the ball, for 
the length of the pendulum. 

2. The Physical Pendulum. Clamp the knife-edge at the 
end of a physical pendulum consisting of a cylindrical rod; 
then, at a distance of three or four centimeters from the end; 
and so on, until within a few centimeters of the center of 
gravity of the pendulum. The period of vibration should be 
determined by taking the time of about one hundred vibra- 
tions. 

Data* — 1. (1.) L si the length of the simple pendulum; (2.) 
N s , the number of vibrations counted; (3.) T sy the time of 
the number of vibrations counted; (4.) P s , the time of one 
vibration; (5.) g; gravity. 

2. (1.) L p , the distance from the knife-edge to the center 
of gravity of the physical pendulum; (2.) N py the number of 
vibrations counted; (3.) T p , the time of the number of vibra- 
tions counted; (4.) P p , the time of one vibration. 



Curve. — Plot a curve with the distances from the center of 
gravity of the physical pendulum as abscissas, and the corres- 
ponding values of the time of one vibration as ordinates. 



26 FOR CES OF NA Tl T RE.—IN LIQ I T IDS. 

EXPERIMENT io. 

COHESION, ADHESION, SURFACE TENSION, CAPILLARITY 





Jl 



Capillar}- Tubes. 

Method. — I. Cohesion and AdJiesion. Suspend a plate of 
glass beneath one scale-pan of a beam balance, by means of 
threads attached to its circumference. The plate should be 
well cleaned, and should be held in a horizontal position. 
After balancing the plate with weights, lower it upon the sur- 
face of water. Now add weights to the opposite scale until 
the plate is separated from the water. 

2. Surface Tension. Wipe two needles with a greased cloth, 
and place them parallel and near together on the surface of 
water. Then place a drop of alcohol on the surface of the 
water between them, and notice their motion. 

3. Capillarity, (a.) Place a piece of cardboard between 
the edges of two plates of glass about 20 by 10 cm.; with the 
other edges in contact, insert the end into water. Notice the 
rise of the water. 

(b.) Measure the diameter of four capillary tubes of differ- 
ent bore, as in Exp. 1. 

Data* — (1.) -D, the diameter of capillary tube; (2.) R c , the 
rise of cold water; (3.) R,, , the rise of hot water; (4.) R„ , the 
rise of alcohol; (5.) D m , the depression of mercury. 



2s 



FORCES OF NATURE.— IN LIQUIDS. 



EXPERIMENT u. 



SPECIFIC GRAVITY. 



Method* — i. Solids, (a.) Measure the 
volume as in i, Exp. 2, and the weight 
as in 4, Exp. 2. 

(&.) Find the weight of the substance 
by placing it on the upper scale-pan of the 
Jolly balance (the lower one under water), 
then removing it and placing weights 
upon the pan until the same elongation 
is produced. Now place the substance 
in the lower scale-pan, and produce the 
same elongation as before by adding 
weights to the upper scale pan. 

The quotient of the two sets of weights 
placed on the upper scale-pan, is the s. g. of 
the substance. Divide the elongation pro- 
duced when the substance is placed on the 
upper scale, by the change in the elongation 
when it is placed on the lower scale. The quo- 
tient is the s. g. 

2. Liquids, (c.) Hare's Method. Con- 
nect two long glass tubes at the top, and 
dip one into a vessel containing water, the 
other into the liquid whose s. g. is to be 
found. Reduce the pressure in the tubes 
by suction until the liquids stand near the 
top. 

The length of the column of water divided 
by the length of the column in the other tube 

is the s. g. 

(d.) Variable Immersion Hydrometer. 

Data.— (tf.) (i.) V, the volume; (2.) W, 
the weight; (3.) s.g., the specific gravity. 

(fr.) (1.) Wi, the weight that produces an equal elongation; 
(2.) W 2 , the added weight; (3.) E u , the elongation produced 
with the substance on the upper scale-pan; (4.) E,, the 
elongation produced with the substance on the lower scale-pan ; 
(5-) ■*•£"•! the specific gravity. 

(V.) (1.) L w , the length of the column of water; (2.) L s , the 
length of the column of the liquid measured; (3.) s. g., the 
specific gravity. 




Jolly's Balance. 



30 



THE FORCES OF NATURE— IN GASES. 



EXPERIMENT 12. 



BOYLE S LAW 



L tg^B. 




Method, — Pour mercury into the open 
tube until it stands about 1 or 2 cm. in 
each tube. Bring the two columns on 
exactly the same level by inclining the 
apparatus and gently shaking it. Now 
pour mercury into the open tube until it 
stands 10 or [2 em. above the surface of 
the mercury in the closed tube; then pour 
in mercury until it stands about jo em. 
above the mercury in the closed tube; and 
so on, until the long tube is nearly filled. 

The barometric pressure must be taken 
at the time the experiment is performed. 

Data. (I.) /-,, the lengths of air col- 
umn when the level is first secured, and 
at each change in the level of the mer- 
cury; (2.) L mt the corresponding lengths 
of the mercury in the long arm, above the 
level oi the mercury as it stands in the 
short arm; (3.) />, the height of the bar- 
ometer; {4.) J\ the pressure on the con- 
fined air. 

B + L m ~P. 

Curve. Plot a curve with the different 
pressures as abscissas, and the corres- 



Boyle's Law Apparatus 

ponding lengths o\ the air column as ordinates 



32 



THE FORCES OF NATURE.— IN GASES. 



EXPERIMENT 13. 

THE AIR PUMP. 

Method. — (1.) Connect a small receiver with the pump by 
means of a rubber tube. Place the hand firmly on the mouth 
of the receiver, and cautiously 
exhaust a part of the air. 

In using- the air pump, do not 
make short strokes with the handle 
of the pump. Lift the handle until 
the piston is at the bottom of the 
pump. 

2. Place a rubber sack con- 
taining a few ounces of shot, 
in a vessel partly filled with 
water, and exhaust the air. 




3. Place some rubber tubing 
over the end of a sma 



Air Pump. 

tube; by suction, fill the tube with water to within a few centi- 
meters of the top; compress the tubing so that the water will 
remain at this point, and place it in a tall bell jar. Allow the 
lower end of the tube to dip into a vessel of water, and ex- 
haust the air. 

4. Produce a fountain in vacuo. 

5. Exhaust the air from the Magdeburg hemispheres, and 
attempt to pull them apart. 



34 



THE Ft )RCES ( '/•' A . I /'( RE, IX (,\ ISES. 



EXPERIMENT i.|. 



THE SIl'llON. 



Method, Fill a jar with water, and place it on a support [2 
or 1 J in. high. Place a siphon in the jar of" water, and secure 
it in position. Set a second vessel ol water on a table, anil 
use a rubber tube as a siphon to keep the water in the jar at 
a constant height. This may be done by starting the flow 

through the tube ami regulating it by 
pressure o\ the ringers on the tube. 
Start the siphon by suction, and catch 
the How in a graduated cylinder of 
about 500 cubic centimeters capacity. 
Then change the level o( the water in 
the jar, ami proceed as before. The 
flow should be taken in this manner 
for three or four different heights o! 
the water in the jar. 

Data, (I.) //,,., the height o( the 
level oi water above the floor; (2.) 

//, , the height of the long end o( the 
siphon; (3.) I\ the difference in the lengths of the arms of the 
siphon; (4.) '/', the time required for a flow of 500 ccm.; 
(5.) F, , the flow per sec; (6.) A", the tlow per sec. divided 
by the difference in the lengths o( the arms o( the siphon. 

The height oi the level of the water above the lloor minus the 

height of the long arm from the floor, will give the difference in 
lengths of the arms of the siphon. These distances are more easily 
measured than the arms of the siphon. It is better to place a perfor- 
ated rubber stopper containing a piece oi glass tubing that just 

reaches through it, in the end o( the long arm. 




Siphon. 



>, 



ENERGY. 



EXPERIMENT 15. 



PULLEYS, WHEEL AND 








& 



W 



1 



i 



AXLE. 

Method*— 
I. Pulleys. Find 
the power neces- 
sary to raise some 
small load, with 
each set of pulleys. 
The power should 
be such that it will 
maintain a uni- 
form downward 
motion when once 
started. Then find 
the same for a 
little larger 
load, and so on, 
increasing the 
load each time 
until eight or 
ten different 
loads have been 

Pulleys. USed. 

2. Wheel and Axle. Proceed as with the pulleys to find the 
power for the different wheels. 

Data, — 1. (1.) S, the system of pulleys used; (2.) L p , the 
load; (3.) P pt the corresponding power; (4.) P cp , the com- 
puted power; (5.) E p , the efficiency of the pulleys corres- 
ponding to each observation. 

2. (1.) R w , the radius of the wheel; (2.) R a , ,__ 

the radius of the axle; (3.) L w , the load; (4.) c 
P w , the corresponding power; (5.) P cw , the com- 
puted power; (6.) E w , the efficiency of the wheel 
and axle corresponding to each observation. 
P — P — E 

■* cp . J- p ^p ' 

Curves* — Plot three curves, on the same sheet, 
for a set of compound pulleys with loads as ab- 
scissas, and powers, computed powers, and effi- 
ciencies respectively as ordinates. ^ 

The first one is the experimental curve; the second, 
the computed curve; the third, the efficiency curve. Wheel and Axle. 




U 



4 



HEAT 



KXPERIMENT 16. 



FRANKLINS EXPERIMENT, AND LAWS OF BOILING. 



Method* — i. Arrange the apparatus as shown in the figure. 
The retort should be spherical, and the glass tube, about 75 
cm. long. The glass tube and a thermometer are passed 
through a double perforated rubber stopper. The tube just 
reaches through the stopper, and the bulb of the thermometer 
is some distance above the surface of the water. 

Boil the water until the thermometer 
ceases to rise higher. Then dip the end 
of the glass rod into a cup of mercury, 
and at the same time remove the 
source of heat. Now pour a stream of 
cold water over the retort. 

2. Dissolve much salt in water, and 
find the boiling point. (Do not use 
mercury.) 

3. Determine the boiling point of 
water with 
it. 




immonia gas absorbed in 



Apparatus. 



Prepare the water by passing the gas 
from boiling" ammonia water into it. 

Data, — (1.) vS, the substance boiled; (2.) T, the boiling- 
point; (3.) />, the height of barometer; (4.) J/, the height of 
mercury column; (5.) J\ the pressure on the water; {6.) T , 
the corresponding boiling point. 

One experimenter attends to the apparatus in 1, keeping the tube 
vertical; a second one calls off the reading of the theremometer for 
each degree: a third one calls off the corresponding height of mercury' 
in the tube: a fourth one records the readings as called off. 

B — m= r. 



40 HE A T. 

EXPERIMENT 17. 

TO CORRECT THE READING OF A THERMOMETER. 

Method* — 1 . To find the pressure necessary to change the boiling 
point one degree. Arrange the apparatus as in Exp. 16. — The 
thermometer used should be graduated into one-fifth degree. 
Place small rubber bands on the glass tube at distances of 2, 
3, and 4 cm. from the lower end. Boil the water until the 
thermometer remains stationary; then dip the tube into mer- 
cury until the surface of the first band touches the surface of 
the mercury; and continue the boiling until the thermometer 
is again stationary. Similarly determine the boiling point 
when the second band touches the mercury; and then, the 
third one. 

2. Use the thermometer to be corrected, and determine 
the boiling point when the tube is open. 

Data* — (1.) T, the temperature of the boiling point when 
the tube is open; (2.) T 2i the temperature of the boiling 
point under an increased pressure of 2 cm.; (3.) T >f the tem- 
perature of the boiling point under an increased pressure of 
3 cm.; (4.) T A , the temperature of the boiling point under an 
increased pressure of 4 cm.; (5.) P, the pressure necessary to 
change the boiling point one degree; (6.) B, the height of 
the barometer; (7.) T c , the boiling point as shown by the 
thermometer to be corrected; (8.) T 8 , the temperature that 
the thermometer to be corrected would show at the standard 
pressure of 76 cm.; (9.) C, the correction for the ther- 
mometer. 

P is the average of 2-i-(T 2 — T), 3 — (T 3 — T), and 4 4- 
(7^ — T). It has been found to be about 2.68 cm. 

T c + (76 — B)+P=T s . 

1 00 — T s = C. 



42 HE A T. 

EXPERIMENT 18. 

newton's law of cooling. — radiation. 

Method* — i. Newton s Lazv of Cooling: Fill a beaker of 
about 500 ccm. capacity with water about twenty degrees 
warmer than the air of the room, and place it on some poor 
conductor of heat. Take the temperature every two minutes, 
stirring well with a thermometer before each reading. 

2. Radiation. Fit a large test tube with a double perforated 
rubber stopper holding a thermometer and a glass tube. Ex- 
haust the air from it, and place it in a vessel of warm water. 

With the hand near a heated object, notice the difference in 
radiated heat received with and without a plate of glass be- 
tween the hand and the object. Similarly determine whether 
a plate of glass will intercept the heat from the sun. 

Data* — I. (1.) T„, the temperature of the air; (2.) /, the 
time of each reading; (3.) T„, , the corresponding temperature 
of the water; (4.) M, the mass of the water; (5.) H ri the heat 
radiated between observations; (6.) R, the radiation constant 
of the beaker found for each interval between observations; 
(7.) R, , the radiation constant of the beaker. 

2. (1.) T, the temperature before exhausting the air; (2.) 
T e , the temperature after exhausting the air; (3.) 4, the 
time from placing the tube in warm water until the readings 
are taken; (4.) T c , the corresponding temperature. 

M = the number of cubic centimeters of water. 

H r is found by multiplying M by the change in tempera- 
ture. 

R is found by dividing H r by the time between observa- 
tions, and the quotient by the average difference in tempera- 
ture between the water and the air. 

R, is the average value for R. 



44 HE A T. 



EXPERIMENT 19. 

WATER EQUIVALENT OF A VESSEL. 

Method. — Fill the beaker used in the last experiment about 
two-thirds full of water about five degrees cooler than the air 
of the room. Stir the water constantly with a thermometer 
until the water and beaker have the same temperature. Then 
add water about twenty degrees warmer than the air of the 
room until the beaker is nearly full. Stir the water constant- 
ly until the temperatures are equalized. 

Data* — (1.) M Ci the mass of the cold water; (2.) M w , the 
mass of the warm water; (3.) T Ci the temperature of the cold 
water immediately before the warm water is added; (4.) T iry 
the temperature of the warm water immediately before it is 
added; (5.) T m , the temperature of the mixture; (6.) IV, the 
water equivalent of the vessel. 

The heat given off by the warm water must equal that re- 
ceived by the cold water and the beaker. The change in 
temperature of the warm water is T„, — T m . The change in 
temperature of the cold water and the beaker is T m — T c . The 
water equivalent of the vessel can be found from the follow- 
ing equation: — 

(M c + W) (T m —T c ) =M„, (T w —T m ). 



46 HE A T. 



EXPERIMENT 20. 

SPECIFIC HEAT. 

Method. — Suspend a loose coil of wire weighing about 400 
g. in boiling water. Let it remain until it has attained the 
temperature of the water. Remove the coil and, as quickly 
as possible, place it in the beaker used in Exp. 19, containing 
about 400 g. of water. The temperature of the water should 
be about the same as that of the room. Stir the water con- 
stantly until the temperature ceases to rise, and for one 
minute after it begins to fall. 

Data* — (1.) M et the mass of the coil; (2.) M w , the mass of 
the cold water; (3.) T c , the temperature of the coil as shown 
by the boiling water; (4.) T w , the temperature of the cold 
water; (5.) T m , the temperature of the mixture at the time 
it ceases to rise; (6.) /, the time occupied in equalizing the 
temperatures; (7.) T lt the temperature of the mixture one 
minute after it begins to fall; (8.) IV, the water equivalent of 
the beaker; (9.) 7,, the temperature of the mixture corrected 
for radiation; (10.) H c , the heat lost by the coil; (11.) H ly 
the heat necessary to change the coil one degree; (12.) S, 
the specific heat of the coil. 

The water equivalent of the beaker is obtained from the 
data of Exp. 19. 

T m + t(T m —T 1 ) + 2 =T r . 
(T r —T ir ) (M w + W) —H c . 

ff 1 .^-M e = S. 



48 HE A T. 



EXPERIMENT 21. 

LATENT HEAT OF FUSION OF WATER. 

Method* — Pour about 350 g. of water at about 8o°, into the 
beaker used in the previous experiments. Stir the water with 
a thermometer until the beaker has attained the temperature 
of the water. Now stir it for one minute, and, at the end of 
the minute, add about 100 g. of ice. The ice should be 
broken in small pieces, and allowed to remain in the room 
until it has begun to melt. Wipe it with a dry cloth, and im- 
mediately place it in the water. Stir the ice and water con- 
stantly with a thermometer, and continue to stir for one 
minute after the ice is melted. 

Data. — (1.) M w , the mass of the warm water; (2.) M f , the 
mass of the ice; (3.) T y , the temperature one minute before 
the ice is added; (4.) 7^,'the temperature when the ice is 
added; (5.) T m , the temperature when the ice is melted; (6.) 
t x , the temperature one minute after the ice is melted; (7.) 
/, the time required to melt the ice; (8.) W, the water equiv- 
alent of the beaker; (9.) T ct the temperature of melting, 
corrected for radiation; (10.) C if the calories of heat con- 
sumed by the ice; (11.) C, the calories consumed in raising 
the temperature of the ice after melting; (12.) L, the latent 
heat of fusion of water. 

The mass of the ice is found by subtracting the mass of the 
warm water from the mass of the water after the ice is melted. 

(M„+ W) (T w —T c ) = C ; . 
M<X T c = C. 



50 



HE A T. 



EXPERIMENT 22. 

LATENT HEAT OF VAPORIZATION. 

Method, — Place about 400 g. of water, io° cooler than the 
air of the room, in the beaker used in the previous experi- 
ments. Boil the water in a retort arranged as shown in the 
figure, until steam escapes from the tube. Then dip the tube 
near the bottom of the water in the beaker. Stir the water 




Apparatus. 



constantly with a thermometer until it is io° warmer than the 
temperature of the room. Use a thermometer graduated into 
one-fifth degree. 

Data.— (1.) M w , the mass of the cold water; (2.) M a% the 
mass of the steam; (3.) '/]., the temperature of the cold water 
at the time the steam is introduced; (4.) T mi the tempera- 
ture of the mixture; (5.) W, the water equivalent of the 
beaker; (6.) L v , the latent heat of vaporization. 

(M w + w) ('/;„ — '/;.) = m s (100 — '/;„) +m. x L v . 

M s is found by subtracting M from the mass of the heated 
water. 



52 



HEAT. 



EXPERIMENT 23. 

COEFFICIENT OF EXPANSION OF GASES. 

Method* — Attach a funnel tube to the bulb of an air ther- 
mometer as shown in the figure. The tube of the air ther- 
mometer should be about 3 cm. long. Pour mercury into the 
funnel until it will more than fill the rubber tube. Place the 
air bulb in ice water, and cause the mercury to stand at the 
staple holding the tube of the air ther- 
mometer to the support, by changing the 
height of the funnel tube. Transfer the air 
bulb to water at about 20 , and again cause the 
mercury to stand at the staple. Then 
change the temperature to about 40 ; and, 
lastly, to about 6o°. 

When the bulb is transferred to warm 
water, the funnel tube should be elevated un- 
til some mercury enters the air bulb. This 
will prevent any air escaping, by not allow- 
ing the expansion to drive all the mercury 
to the long arm. 

Data. — (1.) T i} the temperature of the 
ice water; (2.) T w , the temperature of the 
warm water at the time the air ceases to ex- 
pand; (3.) B t the height of the barometer; 
(4.) Mi , the difference in the level of the 
mercury in the two columns in ice water; (5.) M„, , the differ- 
ence in the level in the warm water; (6.) C, the coefficient 
of expansion; (7.) A, absolute zero. (See questions.) 

The apparatus must be held vertically when the measurements 
are taken. 

Since the volume of the air is kept constant by increasing the 
pressure, the change of volume that would have occured under con- 
stant pressure is found by the formula: 

B + M s : B + M w :: 1 : V. 
(V-i) +(T W -Td = C. 

Mi will be subtracted, if the mercury stands lower in the funnel 
tube. 




Charles' Law 

Apparatus. 



54 



HE A T. 



EXPERIMENT 24. 

LINEAR EXPANSION OF SOLIDS. 

Method, — Place the rod whose expansion is to be measured, 
through the perforated stopper in the end of the tube, and 
press it firmly against 
the support opposite 
the micrometer screw. 
Connect the wires from 
a cell having an electric 
bell in circuit to the two 
supports. Then turn 
the micrometer screw 
until the ringing of the 
bell shows that con- 
tact has been made. 
Now turn the microm- 
eter screw back one 
or more turns and pass 
steam through the tube. 
Continue this for some 
time after the thermo- 
meter ceases to rise, i 
Bring the micrometer ! 
screw again in contact : 
with the rod. 

Data,— (1.) L, the ex- 
act length of the rod 
at the temperature of 
the room; (2.) 7v, , the 
first reading of the mi- 
crometer screw; (3.) 
R 2 , the second reading 
of the micrometer screw; 
(4.) E y the expansion 
of the rod; (5.) 1\ , the 
temperature when first 
contact is made; (6.) T 2l the temperature when the second 
contact is made; (;.) Q the coefficient of expansion. 




A' R, = h 



E + LtTi— 71) = C 



SOUND. 

EXPERIMENT 25. 

THEORY OF SOUND. 



Method. — 1. Origin of Sound. (1.) Strike a tuning fork 
with a mallet, and bring a light ball suspended by a thread in 

contact with one of the prongs. 

(2.) Attach a bristle to one prong 
of the fork; strike it as before, and 
draw the bristle quickly across a piece 
of smoked glass. 

(3.) Clamp a plate as shown in the 
the figure; sift fine sand over it, and 
draw a bow across the edge of the 
plate. Make different figures by 
touching the plate with the fingers. 

2 . Transmission of Sound. ( 1 . ) Place 
a bell under the receiver of an air 
pump. Notice the effect on the sound 
as the air is exhausted. 

(2.) Partly cover the mouth of a 
sift sand over the rubber, and vibrate 
a timing - fork near the mouth of the tumbler. 




Bell iu Vacuum. 

tumbler with rubber 





Apparatus for Recording Vibrations. 

(3.) Fasten one end of a long spiral spring to a table; hold 
the other firmly in the hand, and rake a small bar a short dis- 
tance along the coil. 

The student should make such observations as will enable him to 
understand thoroughly the questions to aid him in the discussion. 



58 



SOUND. 



EXPERIMENT 26. 



LAWS OF VIBRATING STRINGS. 



Method* — 1. Law of Length. Keep 
the tension on a string of the sonom- 
eter constant, and move the bridge 
until the sound has the same pitch as 
a tuning fork of known vibrations. 
Then move the bridge until the pitch 
is the same as that of a second tuning 
fork; and so on, for different tuning 
forks. 

2. Lazv of Tension . K e e p t h e bridge 
stationary, and bring the string to the 
pitch of each fork by varying the ten- 
sion. 

3. Lazv of Diameter. Vibrate strings 
of the same material but of different 
diameters as in No. I. 

4. Law of Deiisity. Vibrate wires of 
the same diameter but of different 
densities as in No. 1. 



Data* — (1.) T, the tension of the 
string; (2.) L, the length of the string; 
(3.) D, the diameter of the string; 
(4.) d, the comparative densities; (5.) 
V, the number of vibrations as shown 
by the tuning forks. 



60 



SOUND. 



EXPERIMENT 



CHARACTERISTIC PROPERTIES OF MUSICAL SOUND. 



Method, — I. Pitch. Use the siren shown in Exp. 29. Pass 
a current of air through a rubber tube, and hold the end of 
the tube near the inner circle of holes. Keeping the rotation 
constant, successively change the tube to the different circles. 

Similarly notice the effect for dif- 
ferent rates of rotation. 

2. Intensity. Increase the force 
of the current of air through the 
tube, and notice the effect on the 
sound produced by the siren. 

Vibrate a string of the sonometer 
through different amplitudes. 

3. Timber. Pass illuminating gas 



into the flame vibrator, and ignite 
the jet. Attach a mirror to a rota- 
tor, and place it so that the flame 
can be distinctly seen in the mirror 
as it rotates. Now sing any vowel 
sound into the mouthpiece while the mirror rotates. Simi- 
larly obtain the manometric flame when two observers 
sing the same sound, but at different octaves. Try all the 
different sources of sound that are convenient. 

Report. — Draw diagrams representing the flame as observed 
in each trial. 




Flame Vibrator. 



62 SOUND. 

EXPERIMENT 28. 

VELOCITY OF SOUND. 

Method. — Place a glass tube 2 cm. in diameter and about 
40 cm. long, in a jar of water about 35 cm. deep. Vibrate a 
tuning fork near the upper end of the tube, and, by changing 
the length of the air column, find the shortest air column that 
will reenforce the sound of the tuning fork. Find a second 
length of air column that will reenforce the sound of 
the fork. Make the same observations with tubes 4 cm. and 
5 cm. in diameter. The tuning fork should be held at the 
same distance from the mouth of the tube in each trial. 

Data* — (1.) D, the diameter of the tube; (2.) Z x , the length 
of the shortest resonating air column; (3.) Z 2 , the length of 
the second resonating air column; (4.) TV 7 , the number of vi- 
brations of the tuning fork; (5.) T> the temperature of the 
air; (6.) L a , the average length for resonating air column; 
(7.) C, the correction to be made in the length of column per 
centimeter diameter; (8.) Z, the length of air column, cor- 
rected for diameter of tube; (9.) IV, a wave length; (10.) 
V ot the velocity of sound at 0°; (11.) E, the error. 

(l„-L' a ) ^ {£' — £)) = C. 

D and £>' are the diameters of different tubes, and L„ and Z'^the 
respective lengths of air column. The average value found for C in 
the different trials should be taken. 

L a + C X D = Z. 

4 Z:= W. 

NW= V. 
V in meters — .6 T= V . 
332— V — E. 



64 



SOUND. 



EXPERIMENT 29. 

TO DETERMINE THE NUMBER OF VIBRATIONS MADE 
BY A TUNING FORK. 

Method* — 1. By the Siren. Bring the pitch of the siren to 
that of the tuning fork by increasing the number of rotations. 
Use a speed indicator to determine 
the rate of rotation. 

2. By Interference. Connect the 
arms of the interference tube with the 
rubber tubing. Make both arms of 
about equal lengths. Vibrate a tuning 
fork near the mouth of the funnel, and 
change the lengths of the arms until 
no sound is heard at the orifice. 

Data* — 1. (1.) N, the number of 
holes in the disc of the siren; (2.) R, 





Siren. 



Interference Tube. 

the number of rotations made by the disc per sec; (3.) V s , 
the number of vibrations of the tuning fork. 

2, (1.) V, the velocity of sound in air per sec; (2.) 
L s , the length of the short arm; (3.) L ( , the length of the 
long arm; (4.) V, , the vibrations of the fork. 

NR — V s . 
V~2 (A-Z S ) = F/. 

Use a bellows and an air reservoir connected to a rubber tube, to 
furnish the current of air for the siren. 



LIGHT. 

EXPERIMENT 30. 

INTENSITY AND ABSORPTION. 

Method* — I. Intensity. Place a standard candle and the 
light to be measured on opposite sides of the screen. Adjust 
the carriage so that the spot on the screen appears the same 
when viewed from either side. It is better to employ a 
mirror so that both sides may be seen at once. All light but 
that from the two used should be excluded. 




Photometer. 



2. Absorption. To find the per cent of light absorbed by 
window glass. — Find the candle power of a light with and 
without a plate of glass placed over the orifice of the photo- 
meter. 

Data. — I. (1.) D s , the distance of the orifice near the 
standard candle from the screen; (2.) D,. y the distance of the 
orifice near the light to be measured from the screen; (3.) C s , 
the candle power of the standard candle; (4.) C x% the candle 
power of the light. 

2. (1.) C u the candle power of a light; (2.) C g , the candle 
power with the glass over the orifice; (3.) A, the per cent of 
light absorbed. 

Di : D\ :: C, : Q. 
(C\ — C 9 )+C=A. 



68 



LIGHT. 



EXPERIMENT 31, 



REFLECTION AND REFRACTION. 



Method* — 1. Reflection. Pass a ray of light through the 
opening in the center of the reflection apparatus, and change 
the mirror to different angles. The pointer is to be normal 
to the mirror. The arc from the opening to the pointer is 
the angle of incidence; the arc from the reflected spot to 
the pointer is the angle of reflection. 





Reflection Apparatus. 



Refraction Apparatus. 



Pass the light through the different openings, keeping the 
mirror parallel with the diameter of the semicircle. 

2. Index of Refraction. Pass light through the slit in the rear 
of the refraction apparatus, and notice the angle made with 
the normal. Fill the apparatus with water without changing 
its position, and again notice the angle the spot makes with 
the normal to the surface. 

Data* — 1. (1.) A i} the angle of incidence; (2.) A,., the 
angle of reflection. 

2. (1.) a it the angle the incident light makes with the 
normal; (2.) a r , the angle the refracted light makes with the 
normal; (3.) S ; , the sign of the incident angle; (4.) S r , the 
sign of the refracted angle; (5.) /, the index of refraction. 



LIGHT. 



EXPERIMENT 32. 

FOCAL LENGTHS. 



Arrange 



Method* — 1. Of Double Convex Lens. Arrange a screen, 
lens, and cross wires as shown in the figure, and place a lamp 
back of the cross wires. Then place the screen so that a sharp 
image of the wires will be formed on it. Without changing 
the position of either the object or the screen, find another 




Apparatus. 

position for the lens that will give a sharply defined image. 

2. Of Concave Mirror. Place a piece of white paper in 
the eye of a needle, and use it as an object. Start some dis- 
tance from the mirror and bring the needle up until the 
image of the paper and the paper itself do not change 
their relative positions when the eye is moved. 

Data* — 1. (I.) D > the distance from the object to 
the screen; [2.) D, , the distance between the two positions 
of the lens; ($.) F lt the focal length of the lens. 

2. (i.) D pi the distance of the paper from the mirror;" (2.) 
T, the thickness of the mirror; (3.) F mt the focal length of 
the mirror. 

(T>--ir;) -^ 4 I\=F,. 
(I), .+ •/■) -r2=F m . 



72 



LIGHT. 



EXPERIMENT 33. 



PRODUCTION OF COLORS. 



Method* — i. By Refraction. Admit a beam of light through 
a small opening into a darkened room. Place the oscillating 
prism in the path of the beam and throw the refracted light 
on a screen. Form a band of light by oscillating the prism. 

View brightly illumin- 
ated objects by holding a 
prism in front of the eyes. 

2. By Absorption. Mix 
some different colored 
pigments. 

To a solution of po- 
tassium ferrocyanide add 
a little ferric chloride. 

To a solution of potas- 
sium sulphocyanide add a 
little ferric chloride. 

3. By Interference. 
Cover a plate of glass 

with collodion, and make 

a vertical line through the 

collodion with the point 

of a needle. Place a light 

back of the vertical line, and view the line through a vertical 

slit in cardboard. The slit should be about 1 cm. wide. 




Oscillating Prism. 



74 



LIGHT, 



EXPERIMENT 34 



CLASSIFICATION OF COLORS. 



Method, — 1. Primary Colors. Use the rotator and the one 

colored disks of red, green, and violet. Obtain the different 
colors by changing the size oi the uncovered sectors of the 

respective disks. 

2. Complementary Colors. (1.) 

Use two disks having the colors 
oi opposite sectors in 4. In 
this manner, prove that the op- 
posite sectors represent com- 
plementary colors. 

(2.) Place two colored cards 
a few centimeters apart. Hold 
a plate of glass vertically be- 
tween them, and view one card 
by transmitted li^ht, the other 
by reflected light so that the 
two overlap. Prove that the op- 
posite sectors represent com- 
plementary colors, by changing 
the height of the plate of glass. 
3, Subjective Colors. Eix the 
eyes tor one-half minute on a spot at the center oi a red pic- 
ture. The picture should be in strong light. Then fix the 
eyes on a spot at the center oi a white card held in less in- 
tense lisrht. 




Color Uisks. 

One color disk. 
Prismatic colors. 
Primary colors. 
Com pie me 11 1 a r y COlo rs. 



76 



LIGHT. 



EXPERIMENT 35. 

SPECTRA. 

Method* — 1. Bright Line Spectra. In the colorless flame of 
a blowpipe or bunsen burner, insert a strip of asbestos moist- 
ened with a strong solution of salt. Observe the spec- 
trum by means of the spectroscope. In like manner obtain 
the spectra of borax and strontium. 




Spectroscope. 



2. Continuous Spectra. Observe the spectrum of any arti- 
ficial source of light, such as a candle, glow lamp, or gas jet. 

3. Absorption or Dark Line Spectra. Obtain a continuous 
spectrum as above; and then, the spectrum from the same 
source when the light is transmitted through blue cobalt glass, 
or a piece of glass colored red by sub-oxide of copper. The 
colored glass should transmit a greater part of the light. 



MAGNETISM. 

EXPERIMENT 36. 

LINES OF FORCE AND MAGNETIC FIELD. 

Method* — Place a plate of glass on a bar magnet, and sift 
iron filings over the surface of the glass. Compare the di- 
rections of the lines of force as shown by the arrangement of 
the filings, with that shown by a small magnetic needle placed 
in different parts of the field. 

Map, in the space below, the lines of force as shown by the 
filings for the following fields: — 

(1.) || to a bar magnet; (2.) J_ to the pole of a bar mag- 
net; (3.) J_ to the poles of a horseshoe magnet; (4.) J_ to 
the poles of two horseshoe magnets with their poles forming a 
square; (5.) || to a horseshoe magnet; (6.) _L to two north 
poles of bar magnets. 

Magnetic Fields. — 



80 MAGNETISM. 



EXPERIMENT 37. 

INDUCTION AND METHODS OF MAGNETIZATION. 

Method. — 1. Induction. Map a field parallel to a bar of 
soft iron with its center resting on a pole of a bar magnet. 

Form a magnetic chain at one pole of a strong magnet, and 
then slide the opposite pole of another magnet up toward the 
chain. 

2. Methods of Magnetization. (1.) Draw one pole of a bar 
magnet from one end of a bar of steel to the other. Repeat 
this several times, and on opposite sides of the bar of steel. 
The magnet should be lifted some distance from the piece of 
steel as it is returned. 

(2.) Place the opposite poles of two bar magnets together 
on the center of a bar of steel, and draw them simultaneously 
from the center to the opposite ends. Repeat as in (1.). 

(3.) Arrange the magnets as in(2.),but with a piece of wood 
or cork between them. Incline the magnets until they make 
an angle of about fifteen degrees with the bar of steel. Now 
move them together to one end of the bar of steel and back 
to the opposite end several times without lifting them. Lift 
the magnets off from the middle of the bar. 

(4.) Wind some insulated wire spirally around a piece of 
iron, and pass the current from a cell through the coil. 



82 



MAGNETISM. 



EXPERIMENT 38. 

LAWS OF MAGNETIC FORCE. 

Method, — 1. Present the poles of a bar magnet succes- 
sively to the end of a magnetic needle. Repeat the process 
at the other end of the needle. 

2. Vibrate a short needle, having no 
magnets near it, in the earth's field. 
Then place a long bar magnet with its 
south pole two inches from the north pole 

ain vibrate the 
arcs. Similarly 




Mag-nels. 



of the needle, and a 
needle through short 
vibrate the needle when 'he magnet is 
three inches from it; and then, when the 
magnet is four inches from the needle. 

Data, — (I.) V, , the number of vibra- 
tions made by the magnet per sec, due 

to the earth's field; (2.) V 2l the number 

of vibrations with the magnet two inches 

from the end of the needle; (3.) V 8t the 

vibrations with the magnet at a distance 

of three inches; (4.) V it the vibrations 

with the magnet at a distance of four 

inches; (5.) F 2 , the force assumed for 

the field produced by the magnet at a 

distance of two inches from its pole; (6.) 

F :u the relative force of the field at a dis- 
tance of three inches; (7.) i^, the rela- 

_^— — ^-^^ p tive force of the field at a distance of four 

inches. 

Assuming- the strength of the field of the 
mag-net at a distance of two inches to be 1, the 
relative forces of the field at three and four 
inches is obtained from the following- propor- 
tions: 

V\—V\\V\—V\\\\\ F,. 

Mag-netic Needle. ' J — ' , • '4 — v~ •• I • F 4 . 




Magnetic Needle. 




STATIC ELECTRICITY. 

EXPERIMENT 39. 

ELECTROSTATIC INDUCTION. 

Method. — Connect the sphere of a leyden jar with one of 
the terminals of a Holtz Machine, by means of a wire, and 
place the end of the insulated conductor about two centimeters 
from the sphere. Investigate the nature of the charge on the 
sphere and the different parts of the cylinder, with a posi- 
tively charged pith ball or with a proof plane and a gold leaf 





Insulated 

Conductor. 



Leyden 



Jar. 



electroscope. Keep the cylinder insulated; remove it some 
distance, and again test as before. Now touch the cylinder 
when it is near the sphere with the finger, and test as before. 

Data* — (1.) C Si the charge on the sphere; (2.) C i} the in- 
duced charge on the end of the cylinder near the sphere; (3.) 
C rf the repelled charge on the end opposite the sphere; (4.) 
Cj , the charge on the cylinder after the first removal from the 
sphere; (5.) C 2 , the charge on the cylinder after the second 
removal from the sphere. 



86 



S ATIC .'7 ECTRICITV, 



EXPKRIMKN l .40. 



CONPKNSKRS. 



Method, 1. Charge .1 leyden jai twice by each of the Eol 
Lowing methods, and dischargeit, first, by alternately touch 
ing the coatings with a discharger; secondly, by connecting 
the coatings with the discharger: (1.) insulate the jar, and 
connect one coating with a terminal oi the Holt? Machine. 

(2.) insulate the jar, and connect the two coatings to opposite 

terminals of the Holt. Machine. (3,) hold the 
jar with the outer coating in the hand, and the 
other coating connected with the llolt. Machine 

Cinder no eireniustanees should the student make 
connections with both coatings of .1 charged jar, so that 
tiu x charge will pass through him, 

Charge a jai with movable coatings as in 
(3.); place it on aw insulated support) remove 
the two coatings separately; test them with a 
Leyden Jai charged pith ball; place them together, ami again 

wuii Movable o I t b & 

Coatiairs, p U t them in place, Connect the coatings with a 
discharger, 

3, Connect the coatings oi a charged jar with a dis 
charger, and, aftei some tune, again connect them. 




88 



STATIC ELECTRICITY. 



EXPERIMENT 41. 

THE HOLTZ MACHINE. 



Method. — 1 Rotate the machine until it is charged, and test all 
parts of it with a pith ball of known charge. 

2. Rotate backward a few turns, then again forward until charged, 
and again test. 




Toepler-Holtz Machine. 

3. Observe the effect on the discharge in the following cases: (1.) 
with the leyden jars removed; (2.) with the crossbar removed; (3.) 
with the leyden jars removed and the terminals connected to two ver- 
tical tin plates suspended by silk threads. Vary the distance the 
plates are separated from 1 cm. until further separation produces no 
effect. 

4. Use large leyden jars, with the terminals separated until no spark 
will pass. Rotate the plates until the jars are charged; then slip off 
the belt, and stop the rotation of the plate. 



90 



ST A TIC ELECTRICTY. 



EXPERIMENT 42. 

THE EFFECTS OF THE DISCHARGE. 

Method* — 1. Mechanical. Attach one of the terminals of 

the Holtz Machine to an electric whirl. 

Place a card between the terminals of the Holtz Machine, 

and pass a spark. 

2. Physiological. Form an insulated stool by placing a 

board on four tumblers that have been heated until thoroughly 

dry. Let one person 
stand on the stool 
and, while holding 
one of the terminals 
of the Holtz Ma- 
chine, bring his 
knuckle near the 
knuckle or the nose 
of one of the other 
observers. 

3. Heating. Fit a 
test tube with a per- 
forated stopper hold- 
ing a jet delivery 
tube. Place some 

pieces of zinc and some dilute sulphuric acid in the tube, and 

ignite the jet by bringing it between the knuckles held 

as in 2. 

4. Luminous. In a dark room notice the discharge, (1.) 
from the combs; (2.) from the combs after a few backward 
rotations; (3.) through Geissler tubes. 

Duration of Spark* — In a dark room, observe the carriers by 
means of the spark. Vary the distance between the terminals 
until the carriers appear to remain stationary when viewed by 
rapid sparking. The carriers will appear to rotate slowly 
backward or forward, if the distance between the terminals be 
made less or greater. 




Geissler Tubes. 



THE ELECTRIC CURRENT, 



EXPERIMENT 43. 

EFFECTS OF CURRENT. 

Method* — I. Pass a wire carrying a strong current perpen- 
dicularly through a piece of cardboard, and sift iron filings 
over the cardboard. 




Decomposition 

Apparatus. 




Ampere's Frame. 



2. Amperes Laws. — Use Ampere's 
Frame, and observe the effects produced 
in each of the following cases: (1.) when 
the current through wires free to move 
are parallel and in the same direction; 
(2.) when they are parallel and in op- 
posite directions; (3.) when they are an- 
gular. 

3. Bring the end of a solenoid carry- 
ing a current near the end of a magnetic 
needle. 

4. Hold a straight wire carrying a cur- 
rent parallel to a magnetic needle. 

5. Pass a current through a solution 
of starch paste and potassium iodide. 

Rub down some starch in a little water and 
boil. Add much water and a little 
ootassium iodide. 



6. Pass the current from 
four cells arranged in series 
through the decomposition ap- 
paratus containing water acid- 
ulated with sulphuric acid. 



94 



THE ELECTRIC CURRENT. 



EXPERIMENT 44. 

LAW OF THE TANGENT GALVANOMETER. 



Method* — Place a tangent galvanometer with the coils of 
its windings in the magnetic meridian. Connect a resistance 
box in series with it, and pass the current from two or three 
cells in series through the greatest resistance that will give a 
deflection large enough to be read. Make ten or twelve read- 
ings, diminishing the resistance each time. The last reading 

should be taken with no resist- 
ance through the box. Now re- 
verse the current, and starting 
with no resistance find the de- 
flection for the same resistances as 
before, but in the inverse order. 

Data* — (1.) R, the resistance 
through the box; (2.) D d , the 
corresponding deflection with the 
direct current; (3.) D r , the cor- 
responding deflection with the 
reversed current; (4.) D my the 
mean deflection for the two sets 
of readings; (5.) Tan., the tan- 
gents of the mean deflections; 
(6.) Cot., the cotangents of the mean deflections; (7.) V, the 
voltage of the cells; (8.) A, the current in amperes; (9.) C, 
the constant of the galvanometer. 

Curves* — 1. Plot a curve with the resistances through the 
box as abscissas, and the corresponding cotangents of deflec- 
tion as ordinates. 

2. Determine the current by the method shown in Exp. 
45, and plot a curve with tangents for abscissas, and the cor- 
responding currents as ordinates. 

Fis obtained by the use of a voltmeter. 
The method of finding- A and Cis shown in Exp. 45. 




Si 

Tangent Galvanometer. 



0(, 



THE ELECTRIC CURRENT. 



EXPERIMENT 45. 

CALIBRATION OF A GALVANOMETER. 

The current flowing in Exp. 44 may be determined from 
Ohm's law. Prolong- the cotangent curve until it intersects 
the horizontal axis. The distance from the origin to the in- 
tersection represents the resistance outside the resistance box. 
Add to this the resistance in the box for the total resistance. 

If the current for any deflection 
be divided by the tangent of the 
angle, the quotient is the current 
that will make the tangent of the 
angle of deflection one. One is 
J ^ (1 T ) tue tangent of 45 . The current 

that will deflect a tangent gal- 
vanometer 45 , is called the con- 
stant of the galvanometer. — The 
average of several values should 
be taken as the constant. 

Method. — Connect the appara- 
tus as shown in the figure. Ad- 
just R so that the deflections of 
be increased about four degrees 




T, Tangent Galvauometer. 

G, Galvanometer to be calibrated. 

5", Shunt. 

R, Resistance Box. 

A', Key. 



the tangent galvanometer wi 
at each reading. 

Data. — (1.) D„ , the deflection of the galvanometer to be 
calibrated; (2.) D, , the corresponding deflections of the tan- 
gent galvanometer; (3.) T, the tangents of deflection of the 
tangent galvanometer; (4.) C, the constant of the tangent 
galvanometer; (5.) A, the current in amperes for each de- 
flection. 

CX T=A. 

Curve* — Plot a curve with deflections of the galvanometer 

to be calibrated as abscissas, and the corresponding currents 

as ordinates, 

See directions for determining- the scales to be used for abscissas 
and ordinates. 



98 



THE ELECTRIC CURRENT. 



EXPERIMENT 46. 



LAW OF SHUNTS. 



Method*— Connect the galvanometer that has been calibrat- 
ed, as shown in the figure. With a small resistance in r in- 
crease the resistance in R until the deflection is about 1°. 
Leaving R constant, make successive changes in r until a 
large deflection is obtained; then remove r and take the 
deflection. 

Data. — (1.) R, the different re- 
sistances" in r; (2.) D t the corres- 
ponding deflections; (3.) A, the 
current through the galvanometer 
corresponding to each deflection 
— found from the curve of Exp. 45. 

Since the changes made in r 
will produce but little change in 
the total resistance, the current 
corresponding to the deflection 
with r removed may be regarded 
as the total current flowing 
through the circuit at all times. 




/ 




III 



/?, Resistance Box. 

>-, Resistance Box for Shunt. 

G, Shunted Galvanometer. 



Curve* — Plot a curve with the resistances in r as abscissas, 
and the corresponding currents through the galvanometer as 
ordinates. Draw a heavy horizontal line at a distance above 
the horizontal axis corresponding to the current flowing when 
r is removed. 



100 



THE ELECTRIC CURRENT. 



EXPERIMENT 47. 

ARRANGEMENT OF CELLS. 

Method. — Arrange six cells of nearly constant electromo- 
tive force in series as in 1. Connect them through an am- 
meter and a resistance box. The galvanometer that has been 
calibrated may be used instead of the ammeter, provided the 

resistance through the circuit is low. 
Find the current with no resistance in 
R\ then with .1 ohm resistance; and 
so on, until R is about equal to the in- 
ternal resistance of the series. 
^ ] Then use the same cells connected 

I I ill || * n two parallel series, and find the cur- 

rent for the same resistances as were 
used when they were in series. Simi- 
larly find the current when they are in 
parallel. 



/ 



1 1 



Mil 

-lllllr-J 

HIiliH . 

2. 

-if- 

L|JJ 



A, Ammeter. 

1, Series. 

2, Two Series. 

3, Parallel. 



Data* — (1.) R h , resistance through 
the box; (2.) R a , the resistance of the 
ammeter; (3.) R c , the internal resist- 
ance of one cell; (4.) R s , the internal 
resistance of the series; (5.) R 2s , the 
internal resistance of the two series; 
(6.) R p , the internal resistance of the 
cells in parallel; (7.) C s , the current 
corresponding to each resistance, when 
the cells are in series; (8.) C 2s , the 
current from two series; (9.) C p , the 
current from the cells in parallel. 

Rc and R a are obtained from the in- 
structor. 

Curves* — Plot, on the same sheet, a curve for each arrange- 
ment of the cells with the external resistances as abscissas, 
and the corresponding currents as ordinates. 



1 



ELECTROMOTIVE FORCE. 

EXPERIMENT 48. 

ELECTROMOTIVE FORCE OF CELLS. 

Method* — 1. Ohvi s Method. Connect a cell of nearly con- 
stant electromotive force in series with a resistance box and 
the calibrated galvanometer. Observe the deflections for dif- 
ferent resistances. 

2. Beeiz's Method. Connect the apparatus as shown in the 
figure. Place the cell whose E. M. F. was measured by- 
Ohm's method so that the E. M. F. of 
/^T\ the cell and that of the battery will act 

L. J in opposite directions through the gal- 

G i- \ x vanometer. Adjust R and r so that 

! — p ~ ^==d — j when the circuits are completed there 

will be no deflection of the galvanom- 
eter. 

Data* — 1. (1.) R g , the resistance of 
"'''■' the galvanometer; (2.) R h , the differ- 

b, Battery. e nt resistances through the box; (3.) 

g, Galvanometer. A. the corresponding deflections of 

the galvanometer; (4.) A, the corre- 
sponding current; (5.) E, the electromotive force of the cell. 

2. (1.) R, the resistance through R; (2.) r, the resistance 
through >; (3.) E c , the electromotive force of the cell; (4.) 
E h , the electromotive force of the battery. 

A =E^r (R h + R g + R c ). 

R c is the resistance of the cell. By substituting two different val- 
ues of A and the corresponding- ones of Rh in the equation, two equa- 
tions containing- the two unknowns E and R c are obtained. From 
these equations E is determined. The average of three or four values 
should be taken. 

E, = E,\r^ (ie + r+iC,)]. 

Rb is the resistance of the battery. Substitute two different val- 
ues for R and r, and solve for Eb. 

Rgis obtained from the curve, Exp. 46; A, from the curve, Exp. 45. 



104 



ELECTROMOTIVE FORCE. 



EXPERIMENT 49. 



FALL OF POTENTIAL OVER A WIRE CARRYING A CURRENT. 




Method* — Connect the apparatus as shown in the figure. 
Place about 50 ohms resistance in r, and adjust R so that 

when contact is made at 5 centi- 
meters the deflection will be 
about 1 degree. Leaving r and 
R constant, make contact at 5 
cm.; then at 10 cm.; and so on, 
increasing the length of the wire 
at each observation. 

Data* — (1.) L w , the different 
lengths of the wire; (2.) D gy the 
corresponding deflections of the 
galvanometer; (3.) T, the tan- 
gents of deflection; (4.) C, the 
constant of the tangent galvan- 
ometer; (5.) A, the current cor- 
responding to each deflection; (6.) R g , the resistance 
through the galvanometer; (7.) p. d., the potential difference 
corresponding to each observation. 

A (R g + >)=/. d. 

R fJ is obtained from the instructor. 

Curve* — Plot a curve with the different lengths of the wire 
as abscissas, and the corresponding potential differences as 
ordinates. 



T, Tangent Galvanometer. 
W, Thin Wire and Scale. 
S, Sliding- Contact Maker. 



106 



ELECTROMOTIVE FORCE. 



EXPERIMENT 50. 



POLARIZATION. 




Method* — I. Clean thoroughly two copper plates and a 
zinc plate. Arrange them in water acidulated with sulphuric 
acid, as shown in the figure. Do not allow them to touch one 
another either inside or outside the liquid. Connect the two 
copper plates through a sensitive galvanometer by means of 
a key, and notice whether any current is 
flowing. Open the key, and short circuit 
the zinc and one of the copper plates for 
some time. Disconnect the copper and 
zinc, and again make contact with the key. 

2. Pass the current from a cell that 
polarizes rapidly, through a tangent galvan- 
ometer. Keeping the circuit closed, take 
the deflection every twenty seconds for two 
minutes. Break the circuit, allow the cell 

to rest for two or three minutes, and again proceed as before. 

Continue for fifteen or twenty minutes, varying the periods of 

open and closed circuit. 

Data. — (1.) T, the time from the beginning of the exper- 
iment to each reading; (2.) D, the corresponding deflections; 
(3.) R, the time for the beginning and end of each period 
of rest. 

Curve* — Plot a curve with the values of T as abscissas, and 
the corresponding values of D as ordinates. Connect the 
points on the curve representing periods of rest, by dotted 
lines. 



G, Galvanometer. 



RESISTANCE, 



EXPERIMENT 51. 



SUBSTITUTION AND DIFFERENTIAL GALVANOMETER. 



LO 



y 



>. 



9 



7?, Resistance Box. 
>-, Resistance to be. meas- 
ured. 
A', Double contact Key. 
<?, Galvanometer. 



Method. — 1. Resistance by Substitution. Connect the ap- 
paratus as shown in the figure. Adjust the resistance through 
the box so that there is no change in 
the deflection when the contact is 
changed. 

2. Resistance by means of the Differ- 
ential Galvanometer. Connect the ap- 
paratus as shown in the figure. If the 
coils are not equally balanced, it will 
be necessary to place a resistance in 
one of the circuits that will produce a 
balance. With no resistance at either R 
or r, adjust a so that no deflection will 
occur when contact is made. The re- 
sistance may need to be placed in 
the circuit with r. Then place R and 
rin circuit, and adjust R so that no 
deflection will occur when contact is 
made. 

Data. — 1. (1.) R/,, the resistance 

through the box necessary to keep 

the deflection constant; (2.) 0, the 

object whose resistance is measured; 

(3.) R , the resistance of the object 

measured — the average value for R h . 

2. (1.) R h , the resistance that 

produces a balance; (2.) 0, the object measured; (3.) 7? ,the 

resistance of the object measured. 




R, Resistance Box. 

r, Resistance to be measured. 

G, Differential Galvanometer. 



110 



RES/STANCE. 



EXPERIMENT 52. 

RESISTANCE IN PARALLEL CIRCUIT. 

Method. — Make the following connections with the slide 
wire bridge: (1.) a battery to the sliding contact and the 
center binding post on the short copper strip; (2.) a resist- 
ance box across the open space on the right; (3.) two heavy 
wires connected by four resistance coils in parallel across the 




Slide Wire Meter Bridge. 

open space on the left; (4.) a galvanometer to the binding 
posts at the ends of the wire. The coils connecting the heavy 
wires should vary in resistance from five to ten ohms. Find a 
position for the sliding contact, such that no deflection of the 
galvanometer occurs when contact is made. In each trial, 
the box resistance should be adjusted so that the point of con- 
tact will be near the center of the wire. 

Data. — (1.) C, the coil or coils in circuit; (2.) R bi the box 
resistance for each coil separately in circuit and when the four 
coils are in parallel circuit; (3.) L r , the corresponding length 
of the wire on the right of the point of contact; (4.) L l} the 
length of the wire on the left of the point of contact; (5.) 
R f , , the resistance of the coils separately and in parallel. 

Since the resistance of the wire varies as its length, the lengths of 
the wire on the right and left of the point of contact may be used as 
resistances. 

L r : L t :: R h : R c 

Designate C by the number on the coil. 



112 



RESISTANCE. 



EXPERIMENT 53. 

SPECIFIC RESISTANCE. 

Method. — Connect the battery to the posts on the right of 
the box, a mirror reflecting galvanometer to the posts on the 
left, and a wire about two meters long to posts in the center. 
Remove the 100 ohms ping from the 
left hand quadrant of the inner semi- 
circle and the 1 ohm plug from the 
opposite quadrant. Read the deflec- 
tions of the galvanometer by means of 
a reading telescope and scale. 

Data. — (1.) L Wf the exact length 
of the wire in centimeters; (2.) D w ,the 
diameter of the wire; (3) R lt the re- 
sistance through left hand quadrant of 




Bridg-e Resistance Box. 



the inner semicircle; (4.) R r , 
the resistance through the right 
hand quadrant; (5.) R Cf the re- 
sistance through outer circle 
when no deflection occurs on mak- 
ing contact; (6.) R wi the resist- 
ance of the wire; (7.) A, the area 
of cross-section of wire; (8.) S,., 
the specific resistance of the ma- 
terial of the wire. 

Specific resistance is the resistance 
of a wire having- a cross-section of one 
square centimeter and a length of one 
centimeter. 

A X R w -f- L„ = S r . 
R t : R, :: R c : R w . 
D w is obtained as in Exp. 1. 




Reflecting Galvanometer. 



114 RESISTANCE. 

EXPERIMENT 54. 

TEMPERATURE COEFFICIENT. 

With the exception of carbon, it is a universal law that the 
resistance of conductors of elementary substances increases 
with the temperature. The resistance of non-metallic liquid 
conductors decreases with an increase of temperature. The 
temperature coefficient is the factor a in the equation: 

R t — R (1 + at) 

R t is the resistance at a temperature of f, and R is the re- 
sistance at 0°. 

Method* — Arrange the apparatus as in Experiment 53. 

1. Use a coil of copper wire of five or six ohms resistance 
for the unknown. The wire should be arranged so that it can 
be placed in a water bath. Place it in water at about 0°, and 
find the resistance of the coil. Change the temperature of 
the water eight or ten degrees by siphoning out some cold 
water and adding hot water. Stir constantly until the coil 
has acquired the temperature of the water. Then again 
change the temperature; and so on, until a temperature of 
about 50 is obtained. 

2. Use an incandescent light for the unknown, and proceed 
as in 1. The resistances out of the different quadrants of the 
inner semicircle will need to be equal in measuring the incan- 
descent light. 

Data* — (1.) 0, the object measured; (2.) t, the temperature 
of the water at each observation; (3.) R,, the resistance 
through the left hand quadrant of the inner semicircle; (4.) 
R r , the resistance through the right hand quadrant; (5.) R e , 
the resistance through the outer circle; (6.) R M , the corres- 
ponding resistance of the unknown; (7.) a, the temperature 
coefficient. 



116 



INDUCED CURRENTS. 



EXPERIMENT 55. 

DIRECTION OF INDUCED CURRENTS. 

Method* — 1. Connect a galvanometer to the secondary coil 
of an induction coil. The coil should be placed three or four 
meters from the galvanometer. Then thrust the end of a bar 
magnet into the coil, and notice the deflection of the needle. 
When the needle is again at rest, quickly withdraw the mag- 
net, and notice the deflection. Similarly obtain the effects 
when the other end of the magnet is used. 




Induction Coils. 



2. Place the primary coil in place, and connect it with a 
cell and contact key. Observe the deflection on completing 
the circuit. When the needle has come to rest, break the cir- 
cuit, and notice the deflection. 

Data* — (1.) W, the direction of the windings of the sec- 
ondary coil; (2.) P, the pole of the magnet used; (3.) D, the 
direction of the motion of the magnet; (4.) D g , the direction of 
the corresponding deflection of the galvanometer; (5.) C m , 
the theoretical direction of the current around the magnet; 
(6.) C iy the corresponding direction of the induced current, 
whether in the same or the opposite direction to the theoret- 
ical current; (7.) C c , the direction of the current around the 
primary coil; (8.) C im , the corresponding direction of the in- 
duced current in the secondary coil when circuit is made; (9.) 
db, the direction when the circuit is broken. 

Use a cell to determine the direction of current corresponding to 
each deflection. 



118 



INDUCED CURRENTS. 



EXPERIMENT 56. 

THE DYNAMO. 

Method. — 1. Connect the hand dynamo so that the field 
windings are in series with a resistance box used for the exter- 
nal circuit. Also connect a voltmeter to the binding posts of 
the external circuit. Adjust a metronome so that its ticks 
will correspond to a moderately rapid turning of the crank. 




Dynamo. 

When the observations are made the number of turns of the 
crank should correspond to the ticks of the metronome. Find 
the voltage for external resistances varying from .1 to 15 
ohms. 

2. Connect the dynamo so that the field magnets will 
have shunt windings, and proceed as with the series windings. 
Vary the external resistance to 40 or 50 ohms. 

Data* — (1.) lV f , the method of exciting the field magnets; 
(2.) R e , the external resistance; (3.) V, the corresponding 
voltage; (4.) C, the corresponding current through the exter- 
nal circuit; (5.) A T , the number of revolutions made by the 
armature per sec. 

V -r- R e = C. 

Curves. — Plot curves on separate sheets with currents as ab- 
scissas, and the corresponding voltage as ordinates. 



QUESTIONS 



TO AID IN THE DISCUSSION OF THE EXPERIMENTS. 



MECHANICS. 

EXPERIMENT 1. 

1. Give directions for reading the different instruments 
used. 

2. Suggest a convenient method of filling the glass tube 
with mercury. 

3. How can the diameter of the tube be found from the 
data? 

4. How would you find the center of curvature of a lens? 

EXPERIMENT 2. 

1. Give the formula used in finding the volume of the glass 
tubing. 

2. Upon what principle does weight by the Jolly balance 
depend? 

3. If the beam balance and the Jolly balance were 2,000 
miles below the surface of the earth, what change, if any, 
would be made from the surface readings in measuring equal 
masses? Why? 

EXPERIMENT 3. 

1. What diameter tends to become the axis of all rotating 
objects? 

2. Why do objects tend to rotate upon this diameter? 

3. If the earth should cease rotating, what change would 
occur in the distribution of the water on the earth? 

4. Disregarding the motion of the earth in its orbit around 



QUESTIONS. 121 

the sun, what path would be made by the earth during each 
revolution of the moon? 

5. Explain the phenomena observed in the experiment 
with the coin and card. 

6. At the center of the earth a rifle ball would weigh noth- 
ing. What effect would this have on the distance it would 
penetrate an object when fired with a given velocity? 

EXPERIMENT 4. 

1. Which one of Newton's laws of motion is illustrated by 
the experiment? 

2. If the apparatus could be lowered into the earth to the 
depth of 2,000 miles, what change would there be in the cen- 
trifugal force? In the weights lifted? Why? 

3. If the apparatus could be placed at the center of the 
earth, where the mass rotating would have no weight, and a 
dynamometer should be substituted for the weights, what 
change would there be in the centrifugal force as found by 
the experiment, and that shown by the dynamometer? Why? 

4. What holds the earth in its orbit? 

5. What effect has the rotation of the earth on objects on 
its surface? Where is the force greatest? Why? 

6. Give the laws of centrifugal force. 

EXPERIMENT 5. 

1. What do you understand by composition of forces? 

2. What are the maximum and minimum values of the re- 
sultants that can be obtained from the forces a and /?? What 
will be the direction of the forces in each case? 

3. Give directions for experimentally resolving a force in- 
to two components, when one component and the angle be- 
tween it and the given force are known. 

EXPERIMENT 6. 

1. Why is the acceleration found by the experiment less 
than gravity? 

2. Give the laws of uniformly accelerated motion. How 
does the experiment demonstrate them? 

3. If a dynamometer be arranged so that it may be used 
instead of the rider to produce the constant force, what 



122 PHYSICAL LABORATORY MANUAL. 

change in the acceleration found by the experiment would be 
produced, if the machine were at the center of the earth, 
where the masses used would weigh nothing? Why? 

EXPERIMENT 7. 

1. Give the laws of gravity. 

2. Give two reasons for the weight of an object increasing 
in going from the equator to the poles. 

3. Show that the first statement under the experiment is 
true. 

4. Show that the proportion will give the equivalent mass 
of the pulley. 

EXPERIMENT 8. 

1. What is a simple pendulum? 

2. What is a compensated pendulum? Why is a compen- 
sated pendulum possible? 

3. In what way will a pendulum show that the earth ro- 
tates? Why? 

4. Show that the experiment demonstrates the laws. 

5. How do the vibrations vary with changes of gravity? 

EXPERIMENT 9. 

1. How measure the height of mountains by means of a 
pendulum? 

2. Where is the point of suspension in a physical, or com- 
pound pendulum for the greatest number of vibrations? 

3. Does the curve show that there are pairs of points of 
suspension that have equal periods of vibration? 

4. What relation between the length of a physical cylin- 
drical pendulum suspended from one end, and that of a sim- 
ple pendulum having the same period of vibration? 

EXPERIMENT 10. 

1. Distinguish between cohesion and adhesion. What 
kind of forces are they? At what distance do they act? 

2. Which breaks in I? When will a liquid wet a solid? 

3. How far below the surface of water must a molecule be 
situated before the cohesive force acting upward equals that 



QUESTIONS. 123 

acting downward? What effect has this on the surface mole- 
cules? 

4. Why do the needles remain on the surface? Why sep- 
arate? 

5. Does surface tension act anything like a rubber cover- 
ing pulling downward on the surface? What would be the ef- 
fect of placing a tube in an opening through the rubber cover? 

6. Since the water wets the tube, and the result is a thin 
film of water covering the inside of the tube, is it in reality a 
capillary tube with walls of water? Would the material of 
the tube, provided the water wet it, have any effect on the rise? 

7. Does the adhesive force of the tube (or the cohesive 
force of the film of water) exert an upward pull on the near 
molecules and thus tend to overcome the surface tension? 
Would this action produce the same effect as the opening 
through the rubber cover? 

8. Give the laws of capillarity. 

EXPERIMENT 11. 

1. Explain each method, and state the principle upon 
which each is based. 

2. Are the spaces on the hydrometer of variable immersion 
equidistant? Why? 

EXPERIMENT 12. 

1. What is Boyle's law? 

2. What does the height of the barometer indicate? Why 
is it necessary to take the reading of the barometer? 

3. What proportion can be formed by using the length of 
the column of air when the mercury stands the same in each 
arm, B, B-\-L m , and the corresponding value of L a . Show that 
the proportion verifies the law. 

4. Show that the curve verifies the law. 

EXPERIMENT 13. 

1. Describe an air pump. 

2. What affect on man has the rarefied air of high moun- 
tains? 

3. Of what use is the air bladder of a fish? How is it con- 
trolled? 

4. In what way could yon tell the degree of vacuum in 3? 



124 PHYSICAL LABORATORY MANUAL. 

5. Why does the stream in the fountain suddenly get 
larger when the water rises above the vent? Would geysers 
act in the same manner? 

EXPERIMENT 14. 

1. What is a siphon? 

2. Given the specific gravity of a liquid, how find the limit 
for the height of the bend of the siphon above the liquid? 

3. What forces tend to make the water flow in opposite 
directions in the siphon? 

4. When are the forces in equilibrium? 

5. What is the law of the flow of siphons? 

EXPERIMENT 15. 

1. What law applies to all simple machines? 

2. Why do not the experimental curve and the calculated 
curve coincide? 

3. Does friction increase with the load? How do the 
curves show it? 

4. What is the efficiency of a machine? 

HEAT. 

EXPERIMENT 16. 

1. What force acting among the molecules of water tends 
to hold them together? 

2. What external force aids this force in keeping them to- 
gether? 

3. What force acting among the molecules tends to separ- 
ate them? 

4. If c be the first force; />, the second; //, the third; what 
equation will show the point at which they will separate? 

5. What would be the effect of increasing pi Of decreas- 
ing p't 

6. Give the laws of boiling? 

EXPERIMENT 17. 

1. Can heights be measured by the boiling point? 

2. If 295 meters in elevation decrease the atmospheric 
pressure 2.68 cm., what formula would be used? 



Or EST/O AS. 125 

Given the pressure as shown by the gauge on a boiler, what 
formula would give the boiling point? 

The gauge shows the pressure above that of the atmosphere. The 
formula should include B. 

4. Could potatoes be cooked by boiling in an open vessel 
when the atmospheric pressure is low: Why? 

EXPERIMENT 18. 

I. What is Newton's Law of Cooling? 
.2. Define radiation constant? 

The definition should be obtained from the method of finding- it. 

3. How find the radiation constant per unit area of a 
substance? 

4. Show that the different values obtained for the radiation 
constant is a test of the law? 

5. What is radiant energy? 

6. What difference in the length of the vibrations of the 
radiant energy received from the hot object and that received 
from the sun? 

7. Why does the temperature in greenhouses during bright 
sunshine in winter, rise much above the temperature of the air 
outside? 

EXPERIMENT 19. 

1. What is understood by water equivalent of a vessel? 

2. Why does the water equivalent for different substances 
vary ? 

3. How find the water equivalent per unit mass? What 
name have you for it? 

EXPERIMENT 20. 

1. What proportion can be formed by using the molecular 
weights of solids and their specific heats? 

2. What does the proportion show in regard to the heat 
consumed per molecule in different solids? 

3. Why the difference between oceanic and continental 
climate? 

EXPERIMENT 21. 

I. What becomes of the heat that produces no change of 
temperature? 



126 PHYSICAL LABORATORY MANUAL, 

2. Since it is stored up in the new arrangement of the 
molecules, what kind of energy is it. 

3. What other name for latent heat does this suggest? 

EXPERIMENT 22. 

1. What force acting among the molecules must be over- 
come before vaporization will occur? 

2. Will cold water evaporate? 

3. Will it require more work to separate the molecules of 
cold water than it will those of hot water? Why? 

4. Is the latent heat of evaporization of water at 0° the 
same as it is at ioo°? 

5. What effect has an increase of pressure on the latent 
heat of vaporization by boiling? 

6. What effect upon the temperature has the condensation 
of the moisture of the atmosphere? 

EXPERIMENT 23. 

1. Why start with air at o°? 

2. Why will salt lower the temperature? 

3. Is there much, if any, cohesion in gases? 

4. What force regulates the volume of a gas when the 
pressure remains constant? 

5. Do the data show that the volume varies as this one 
variable force? 

6. If the gas should continue to be gas until that force 
were made zero, what would be its volume? 

7. What temperature would make its volume zero? 

8. What change in the air would occur before it reached 
that temperature? Would it then obey the law? 

9. What is absolute temperature? Absolute zero? 

10. What is the law of Charles expressed for absolute tem- 
perature? 

EXPERIMENT 24. 

1. What is coefficient of expansion? 

2. How account for expansion? 

3. Will a clock run faster in winter than in summer? Why? 



QUESTIONS. 127 

4. If the coefficient of expansion of glass were greater than 
that of mercury, what change would it make in the fixed 
points of a thermometer? 

SOUND. 

EXPERIMENT 25. 

1. What is the origin of sound? 

2. Does ether transmit sound vibrations? 

3. What effect has the vibration of the prong on the air in 
front of it? 

4. How does an air particle vibrate as regards the direction 
of propagation of the wave? 

5. When the compressed air expands will the motion of 
the air particles carry them past the normal state in the same 
manner as the motion of a pendulum carries it past the center? 

6. Do the crests and troughs of the waves caused by drop- 
ping a pebble in water resemble the condensations and rare- 
factions in sound waves? 

EXPERIMENT 26. 

1. Describe a sonometer. 

2. Give the laws of vibrating strings. 

3. Show by proportions formed from the data that the 
experiment verifies the laws. 

EXPERIMENT 27. 

1. By what properties are sounds distinguished? 

2. Upon what does each depend? 

3. What do you understand by harmonics? How produced? 

EXPERIMENT 28. 

1. Explain resonance. 

2. Why is L a one-fourth of W? 

3. Why does L a decrease as D increases? 

.4. The velocity of sound at o° is 332 meters, and increases 
.6 meter for each degree increase of temperature. Explain 
the formula. 

5. What part of a wave-length is represented by L 2 — L{i 



128 PH YSICA L LAB OR A TOR Y MANUA L . 

6. Explain how different sounds are produced by a slide 
trombone. 

EXPERIMENT 29. 

I. Explain how the siren produces sounds. 
• 2. What is interference of sound? 

3. In order to produce silence, how must the waves meet 
at the orifice? 

4. When the tubes are of the same length, what is the ef- 
fect of rotating a vibrating fork near the opening of the fun- 
nel? Explain. 

LIGHT. 

EXPERIMENT 30. 

1. With a single light, how does the spot appear when 
viewed from the different sides? Why? 

2. What is absorption of light? 

3. If the spot absorbed no light, would there be a place 
where it could not be seen from either side? Why? 

4. What will it show in regard to the light transmitted 
from the two sources when the spot appears the same on each 
side? When does this occur? 

5. What is the law of inverse squares? 

6. In what way besides absorption is a part of the light 
lost when the glass is placed over the orifice? 

7. What becomes of the light absorbed? 

EXPERIMENT 31. 

1. What effect has the elasticity of an object upon the 
relative values of the angle of incidence and the angle of re- 
flection? 

2. Give the laws of reflection. 

3. What is refraction? Index of refraction? 

4. What relation between the index of refraction from one 
substance to another and the velocity of light in the two sub- 
stances? 

EXPERIMENT 32. 

1. What are conjugate foci? 

2. When will an image be formed? 



QUESTIONS. 129 

3. Upon what does the focal length of a mirror depend? 

4. Upon what does the focal length of a lens depend? 

5. Define optical center, and state how it may be found for 
the different lenses. 

EXPERIMENT 33. 

1. What is white light? 

2. Why are the colors separated by refraction? 

3. What is absorption? 

4. Upon what does the color of objects depend? 

5. Explain how the color is obtained by mixing the pig- 
ments? 

6. What is diffraction? Explain how colors are formed by 
diffraction. 

7. How account for the colors seen in soap bubbles? In a 
thin layer of oil on water? 

8. Upon what does the color of a soap bubble depend? 

9. Name five natural optical phenomena caused by re- 
flection or refraction of light. 

10. What is dispersion of light? Irrationality of disper- 



sion 



EXPERIMENT 34. 



1. What are primary colors? 

2. What are complementary colors? 

3. Which card in 2 is seen by reflected light? Which by 
transmitted light? 

4. How do the respective amounts of the reflected and 
transmitted light vary with the incident angle? 

5. Will there be a place where the reflected light equals 
the transmitted light? 

6. What are subjective colors? 

7. Explain how subjective colors are produced. 

8. When a piece of iron is heated, what color first appears? 
What color has the fewest number of vibrations? 

EXPERIMENT 35. 

1. Define the three classes of spectra and state how each 
is produced. 



130 PHYSICAL LABORATORY MANUAL. 

2. What produces the light in a candle flame or a gas jet? 

3. How is the spectroscope serviceable in ascertaining the 
composition of the heavenly bodies? 

4. In what way does the spectroscope reveal the motion of 
the heavenly bodies? How is the rate of motion calculated? 

MAGNETISM AND ELECTRICITY. 

EXPERIMENT 36. 

1. Define lines of force, magnetic field, unit magnetic 
pole, field of unit intensity. 

2. Why do the filings move away from the points near the 
magnetic poles? 

3. The fields as mapped are the resultant of what two 
fields? Will all the lines pass through the magnets? 

4. Are there places in the field due to the magnets, where 
the earth's field is exactly neutralized? How can such points 
be located with the needle? 

5. What change is made in the lines of force by placing a 
piece of soft iron in contact with the pole of the magnet and 
against the glass? What change by moving the soft iron to 
different parts of the field? What does this show in regard to 
the iron? 

EXPERIMENT 37. 

1. What is magnetic induction? 

2. Explain the phenomena observed with the magnetic 
chain. 

3. In each method of magnetization determine the poles 
produced by their action on a needle. State how the in- 
duced poles may be known from the poles used and the direc- 
tion of their motion. 

4. From the experiment with the cell, state how the pole 
may be known by the direction of the current around it. 

5. Where are the poles of a bar of steel when the like 
poles are used as in (2) under methods of magnetization? 

6. What are consequent poles? Salient poles? 

7. One pole of a strong magnet repels the similar pole of 
a weak magnet when it is some distance away, but attracts it 
when they are brought close together. Example. 



QUESTIONS. 131 

8. A bar of soft iron is placed horizontally east and west. 
A compass needle is placed with the north-seeking pole four 
inches to the east of the end of the bar. What change will 
occur in the needle when the west end of the bar is elevated 
until the bar is perpendicular? Explain. 

9. Given a needle suspended at its center of mass and free 
to move in any direction, how would you determine in what 
direction north lies, if the needle be unmarked and you have 
no other means of knowing the cardinal points? 

10. A steel needle is magnetized with the north poles of 
magnets used as in question 5. It is then bent at right angles 
at its center and floated on a piece of cork. How will it set? 

EXPERIMENT 38. 

i. Are all substances affected by magnets? 

2. Distinguish between magnets and magnetic substances. 

3. Suggest some means of separating iron and brass filings. 

4. Give the theory of magnetic fields, and Ampere's theory 
of magnets. 

5. State the laws of magnetic force. 

STATIC ELECTRICITY. 

EXPERIMENT 39. 

1. Define unit charge. 

2. What effect has touching the cylinder? Why? 

3. Give the laws of electrical attraction and repulsion. 

4. Explain the action of a dry piece of paper when heated, 
brushed, and held near the wall. 

EXPERIMENT 40. 

1. What is a condenser? A dielectric? 

2. What are necessary to form a condenser? 

3. Which method of charging gives the strongest charge? 
Why? 

4. What does 2 show? 

5. Why the second spark in 3? 

6. Why does not the whole charge escape when one coat- 
ing is grounded? 

7. Explain the action of an electroscope. 



132 PHYSICAL LABORATORY MANUAL. 

EXPERIMENT 41. 

1. How does the machine build up its charge? 

2. What is the purpose of each of the following: combs, 
carriers, crossbar, leyden jars, armature, brushes? 

3. How do the terminals receive their charge? 

4. Explain the effect of reversing the rotation. 

5. Why the backward rotation in 4? What is the condi- 
tion of the jars after the rotation ceases? 

EXPERIMENT 42. 

1. What peculiarity do you observe in the hole through 
the card? 

2. What effect has rarefied gases on the discharge? 

3. Define cathode and anode? What distinction do you 
observe between the light at cathode and anode? 

4. Why the change in the discharge from the different 
combs when the plate is turned backward a few turns? 

5. Explain the phenomena observed under duration of the 
spark. 

THE ELECTRIC CURRENT. 

EXPERIMENT 43. 

i. Classify the effects you have observed. 

2. Give Ampere's laws. 

3. What is the direction of the current in the end of a 
solenoid that acts as the south pole of a magnet? 

4. Show that Ampere's laws and his theory of magnets 
would cause the needle to behave as observed in 4. 

5. What two gases are formed by the decomposition of 
water? Which has the greatest volume? At which electrode 
does each collect? 

6. What effect has the current on the solution of starch 
paste? At which electrode does the change occur? 

EXPERIMENT 44. 

1. What two magnetic fields influence the needle? 

2. What angle will these fields form when the windings of 
the galvanometer are in the magnetic meridian? 



QUESTIONS. 133 

3. Is this true for any part of the field or just the axis of 
the coil? 

4. Why use a short needle? 

5. What does the variation in the deflections of direct and 
reversed current show in regard to the position of the coils of 
the galvanometer? 

6. How is the resistance of the cells, connecting wires, and 
galvanometer shown by the first curve? 

EXPERIMENT 45. 

1. Upon what does the sensitiveness of a galvanometer de- 
pend? 

2. State how you can determine from the curve drawn, the 
current corresponding to any deflection. 

3. Must the same plugs be out of the tangent galvanome- 
ter as were out in Experiment 44? Why? 

4. In determining a current from the curve of the cali- 
brated galvanometer, must the same shunt always be used? 
Why? 

EXPERIMENT 46. 

1. What are shunts? 

2. What current is shown by the curve for each of the fol- 
lowing distances: (1.) from the horizontal axis to the heavy 
horizontal line; (2.) from the horizontal axis to the curve; 
(3.) from the curve to the heavy horizontal line? 

3. Determine from the curve the resistance in the shunt 
when it Carries one-half of the current. 

4. What will be the relative resistances in the galvanome- 
ter circuit and the shunt when each carry one-half the current? 
What does this show the resistance of the galvanometer cir- 
cuit to be? 

5. What proportion can be formed by using the resistances 
of the shunt and galvanometer circuit and their respective 
currents? 

6. What is the law of the currents flowing through the 
parts of a divided circuit? 

EXPERIMENT 47. 

I. The curve that shows the strongest current, and con- 
sequently the best arrangement of cells, will be located above 



134 PHYSICAL LABORATORY MANUAL, 

the others. Does any arrangement give the strongest current 
for all resistances? 

2. Does each curve at some point lie above all the others? 
What does this show? 

3. Determine from the curves the external resistance for 
each arrangement when it gives the strongest current. How 
do they compare with the corresponding internal resistances 
of the cells? 

4. Give the rule to be followed in arranging cells so as to 
produce the strongest current. 

ELECTROMOTIVE FORCE. 

EXPERIMENT 48. 

1. Upon what does the electromotive force of a cell de- 
pend? 

2. Distinguish between potential difference and electro- 
motive force. 

3. Under what circumstances would the potential differ- 
ence at the terminals of a battery equal the electromotive force 
of the battery? 

4. Since the electromotive force of a cell remains about 
constant, how account for the electromotive force not shown 
at the terminals? 

5. The potential difference between the binding posts of r 
equals the electromotive force of the battery multiplied by 
the quotient of the resistance through r divided by the total 
resistance in the battery circuit. Explain the formula for 
finding the electromotive force of the battery. 

EXPERIMENT 49. 

1. Define potential. 

2. Upon what does the potential difference of two points 
on a wire carrying a current depend? How does it vary? 

3. How does the resistance through the wire compare with 
its length? 

4. Since the galvanometer forms a shunt circuit with dif- 
ferent lengths of the wire, will the external resistance of the 
battery circuit be constant? 

5. How does the curve show this change of resistance? 



QUESTIONS. 135 

6. Under what conditions would the curve be straight? 

EXPERIMENT 50. 

1. What effect have two clean copper plates on the gal- 
vanometer? 

2. What effect have the copper plates after one has been 
short circuited with the zinc? 

3. What collects on the surface of the copper plates while 
short circuited? 

4. Which of the copper plates is electro-positive after 
short circuiting? 

Determine by the direction of deflection as compared with that of 
zinc and copper when the galvanometer is shunted. 

5. How do the hydrogen bubbles affect the electromotive 
force of the cell when zinc and copper are used? 

6. In what other way do they affect the effective electro- 
motive force of the cell? 

7. Name some mechanical methods of preventing polariz- 
ation. 

8. Explain some chemical methods of preventing polariza- 
tion. 

9. Define polarization. 

RESISTANCE. 

EXPERIMENT 51. 

1. How is resistance affected by each of the following: 
length, diameter, material, temperature? 

2. Upon what does resistance by substitution depend? 

3. Describe the differential galvanometer. 

4. Upon what is resistance by the differential galvanome- 
ter based? 

EXPERIMENT 52. 

1. Describe a slide wire bridge. 

2. The resistance through conductors of uniform length 
and material varies inversely as the cross-section. What re- 
lation has the cross-section of each coil to a similar coil hav- 
ing a resistance of one ohm? 



136 PHYSICAL LABORATORY MANUAL. 

3. The reciprocal of the resistance of a conductor is called 
the conductivity. What relation have the answers to 2 to the 
conductivity of the respective coils? 

4. Will the sum of their conductivities show the relation 
of the sum of their cross-sections to the cross-section of a 
wire having a resistance of one ohm? 

5. How does the reciprocal of the sum of their conduc- 
tivities compare with the resistance of the coils in parallel? 

6. How find the resistance due to parallel conductors? 

EXPERIMENT 53. 

1. Which of the following will affect the specific resist- 
ance of a wire: length, diameter, material, temperature? 

2. Why is this means of measuring resistance more accurate 
than the others you have used? 

3. Explain the formula. 

4. Draw a diagram showing the arms of the bridge as you 
have performed the experiment. 

EXPERIMENT 54. 

1. What effect has heat on the distance between the mole- 
cules? Does this suggest a possible explanation for re- 
sistance increasing with the temperature? 

2. But the resistance of an electrolyte decreases as the 
temperature increases. Does this disprove the theory sug- 
gested in i? 

3. If a current be conveyed through an electrolyte solely 
by electrolysis, and heat decreases the chemical affinity 
among the atoms of the molecules of the electrolyte, what 
effect would it have on the resistance of electrolysis? 

4. Is the change of resistance proportional to the change 
of temperature? 

INDUCED CURRENT. 

EXPERIMENT 55. 

1. Give the laws of currents induced by magnetic action. 

2. Give the laws of currents induced by electric currents. 

3. Describe an induction coil. 



QUESTIONS. 137 

EXPERIMENT 56. 

Field Magnets. — I. Distinguish between series and shunt 
windings for field magnets? 

2. What do you understand by a compound winding for 
the field magnets? 

3. The curves drawn are called characteristic curves. How 
do the characteristic curves show residual magnetism in the 
field magnets? 

4. Does increasing the current through the field produce a 
corresponding increase in the voltage? 

Determine from the curve of the series dynamo. 

5. What is magnetic saturation? Will magnetic saturation 
account for the voltage not increasing with the current around 
the field magnets? 

6. Voltage depends on the number of lines of force cut by 
the conductors of the armature and the number of conductors 
on the armature. Give three means of increasing the voltage 
of a dynamo. 

The Armature. — I. Name four kinds of armatures. 

2. The resistance offered to the rotation of the armature is 
called the drag. What causes it? 

3. What is the core of the armature? ■ 

4. If the core of an armature be solid iron there will be 
currents set up in the core. These are called eddy currents. 
Eddy currents are prevented by forming the core in sections 
and insulating them. Should the sections of a drum arma- 
ture be longitudinal or transverse? Why? 

5. Will the magnetic action of the rotating armature set 
up eddy currents in the field magnets? How remedied? 

The Commutator. — I. What is the purpose of the commuta- 
tor? 

2. How are the wires of the armature connected with the 
commutator? 

3. The action of the current in the armature carries the 
points for the location of the brushes around a little in the 
direction of rotation. This is called the lead of the brushes. 
What effect will an increase in the current through the arma- 
ture have on the lead of the brushes? 

4. How are alternating currents taken from the armature? 



PROBLEMS. 



MECHANICS. 



In the following problems gravity at the earth's surface is taken 
as 9.8 meters per sec. Friction is disregarded. 

1. A stone strikes the ground in 6 sec. after it is thrown. 
How high does it rise? Ans. 44.1 m. 

2. A ball is shot vertically upward with an initial velocity 
of IOO m. per sec. In what time will it return to its original 
position? Ans. 20.4 sec. 

3. A stone falls 76 meters in 4 sec. What is gravity? 

Ans. 9.5 m. 

4. A ball is shot vertically upward with an initial velocity 
of 1 17.6 meters per sec; in 8 sec. another is shot with the 
same velocity. How high above the ground will they meet, 
and what will be the velocity of each at that time? 

Ans. 627.2 m., 39.2 m. 

5. A ball is shot vertically upward and rises 93.1 meters 
the first second. How high will it rise? Ans. 490 m. 

6. A stone is thrown into a pit 150 meters deep and 
reaches the bottom in 4 sec. With what velocity was it 
thrown? Ans. 17.9. 

7. A ball is shot upward with an initial velocity of 100 
meters per sec. At the end of 10 sec. its velocity is 10 meters 
per sec. What is gravity, and how high does the ball rise? 

Ans. g is 9 m., and the rise 555.56 m.; or g is 11 m., and the 
rise 454.55 m. 



140 PHYSICAL LABOR A TOR Y MANUAL. 

8. An object weighs ioo g. on the surface of the earth. If 
it be lowered 2,000 mi. into the earth, what force will lift it 
4.9 meters in one second? Ans. 147,000 dynes. 

9. An object at the center of the earth weighs nothing, 
but a constant force of 49,000 dynes is required to move it 
through 9.8 meters in 2 sec. What is its mass? Ans. 100 g. 

10. What constant force will lift 100 g. 4.9 meters in one 
second? Ans. 196,000 dynes. 

11. In an experiment with Atwood's machine, the weights 
were 100 g. and 200 g., and the equivalent mass of the pulley 
was 100 g. What was the acceleration? Ans. 245 cm. 

12. The radius of a wheel is three times that of the axle. 
The power is 700 g. and the load, 1,500 g. With what ac- 
celeration will the power descend? Ans. 166.66 cm. 

13. When the weights used with Atwood's machine were 
7)2 and iyy 2 lb., the acceleration was 12 ft. per sec. What 
will the heavy weight be when the light one is 10 lb. and the 
acceleration, 20 ft. per sec? (The mass of the pulley is not 
considered.) Ans. g is 30 ft.; the heavy weight, 50 lb. 

14. An object weighing 20 g. falls 12,500 cm. in 5 sec. 
What force is acting upon it? Ans. 20,000 dynes. 

15. At what height above the earth's surface will an object 
fall 27 ft. in 3 sec. Ans. 5,267 mi. 

16. The mass of the sun is 332,000 times that of the earth, 
and its diameter no times that of the earth. If a man 
weigh 150 lb. on a spring balance at the surface of the 
earth, what would he weigh at the surface of the sun? 

Ans. 4,116.5 lb. 

17. A pendulum beats seconds. How high above the 
earth's surface must it be raised in order to beat once in 2 
sec? Ans. 4,000 mi. 

18. A board 10 ft. long has one end resting on a car 6 ft. 
high; a cart weighing 1,000 lb. is pulled up the incline by a 



142 PHYSICAL LABOR A TOR Y MANUAL. 

force parallel to the board. With what force does the cart 
press upon the board? Ans. 800 lb. 

19. Three men carry a log uniformly thick and 20 ft. long; 
one carries at the end; the other two with a spike. Where will 
the spike be placed so that each man will carry one-third of 
the log? Ans. 5 ft. from the end. 

20. If A take the long end of a teeter, he will be balanced 
by B on the short end; if he take the short end, he will be 
balanced by C on the long end. If B and C weigh 200 lb. and 
128 lb. respectively, what is the weight of A? Ans. 160 lb. 

21. A box 8 ft. wide, 10 ft. long, and 6 ft. high weighs 500 
lb. How much work will be expended in lifting it on one 
corner, in a state of unstable equilibrium. Ans. 2,035 ft- ^ Ds - 

22. One pound of lead weighs 14 oz. in water. What is its 
specific gravity? Ans. 8. 

23. One pound of lead weighs 14 oz. in water and 14.4 oz. 
in alcohol. What is the specific gravity of the alcohol? 

Ans. .8. 

24. 144 g. of a substance displace 12 ccm. of water. What 
is its specific gravity ? Ans. 12. 

25. How high will alcohol rise in a vacuum to-day? 

26. A piston stands 12 inches from the bottom of an air- 
tight tube. If the area of the piston be 6 sq. in., how much 
work will be done on it to force it down 6 in.? (One atmos- 
phere is taken as 15 lb. per sq.- in.) Ans. 22.5 ft. lbs. 

27. The receiver of an air pump holds 100 cu. in., and the 
barrel of the pump 20 cu. in. What per cent of the air in the 
receiver is removed by one double stroke of the piston? 

Ans. i6# %. 

28. In the experiment with the air pump, an air bubble 
one centimeter long was allowed to remain in the glass tube. 
The tube was 30 cm. long. The air was exhausted until a part 
of the air escaped from the tube, but when the air was ad- 
mitted to the receiver, the air bubble was .75 centimeter long. 



144 PHYSICAL LABORATORY MANUAL. 

What per cent of the air was exhausted from the receiver? 

Arts. 97-5%- 

29. If the earth were a hollow globe, an object at any place 
within the solid shell would weigh nothing. Demonstrate. 

30. Prove that the earth would have to be homogeneous 
throughout in order that for bodies below the surface the 
weight should vary as the distance from the center. 

HEAT. 

1. 100 cu. ft. of air at 50 C. will fill what space at — 50 C? 

Arts. 69.1 cu. ft. 

2. If 100 g. of lead at ioo° C. were placed in 500 g. of water 
at io° C, what would be the resulting temperature? 

A ns. 10.56 . 

3. How much heat will it take to fuse 100 g. of ice at — 20 
C? Am. 9,000 calories. 

4. A locomotive weighing ten tons is running 60 mi. per 
hour. How much bituminous coal would have to be burned 
to produce the energy, if all its heat be transformed into me- 
chanical motion? Ans. .215 lb. 

5. How far would one ton have to fall in order to acquire 
energy enough to convert one pound of ice at — 20 C. in- 
to steam? Ans. 505 ft. 

6. A leaden bullet weighing one ounce is fired with a ve- 
locity of 1,000 ft. per sec. If its temperature when fired be 
20° C, and in collision one-half the energy of the bullet be 
transformed into heat in the bullet, what is the resulting tem- 
perature of the bullet? Ans. 197 C. 

7. A glass tube one meter long and open at one end is 
heated to 137 C. The open end is placed in a cup of mercu- 
ry, and the tube is cooled to 0° C. If the barometer stand at 
76 cm., how high will the mercury rise in the tube? 

Ans. 15.82 — cm. 



146 PHYSICAL LABORATORY MANUAL. 

8. 10 g. of steam at ioo° C. is introduced into 50 g. of ice 
at — 10° C. What is the resulting temperature? 

Ans. 35-3+°- 

9. Find the specific heat of a substance 100 g. of which at 
200°, when placed in 100 g. of water at 20°, raises the tempera- 
ture to 30 . Ans. .0589. 

10. If the pressure on water be such that it boils at 90 C, 
how much heat will it require to vaporize 100 g. whose tem- 
perature is 90 . (The latent heat of vaporization at 90 is 
544-) 

SOUND. 

1. A sound is made at the mouth of a well and in .5 sec. 
the echo is heard. If the temperature of the air be 20° C, 
how deep is the well ? Ans. 86 meters. 

2. With a tension of four pounds, a string vibrates 100 
times per sec. What will be the tension on a string of the 
same material, whose diameter and length are each twice as 
great, when it vibrates 200 times per sec? Ans. 256 lb. 

3. A string vibrating 256 times per sec, and another vi- 
brating 775 times per sec, are sounded together. How many 
beats will be produced by the second overtone of the first and 
the fundamental of the second? Ans. 7. 

4. The velocity of sound in air is 1,000 ft. per sec. What 
is the velocity of sound in hydrogen at the same pressure and 
temperature? (Air is 14.5 times as heavy as hydrogen.) 

Ans. 3,807 ft. 

5. If the wave-length of a sound in air at io° C. be .5 meter, 
how many vibrations are made per sec? Ans. 676. 

LIGHT. 

I. Two lights are 4 meters apart, and their intensities are 
as 1 to Q- How far from the stronger light must a screen be 



148 PHYSICAL LABORATORY MANUAL. 

placed that it may be equally illuminated by them both? 

Ans. 3 meters. 

2. An object is on the axis of a concave mirror and 50 cm. 
from the mirror. The image is 30 cm. from the mirror. 
What is the the radius of curvature of the mirror? 

Ans. 37.5 cm. 

3. The indices of refraction of alcohol and flint-glass are 
1.37 and 1.6 respectively. What is the index of refraction 
from alcohol into flint-glass? Ans. 1.17 

4. The index of refraction of an equi-convex lens is 1.5, 
the radius of curvature 3 ft. What is the focal length of the 
lens? Ans. 3 ft. 

5. A person uses convex spectacles with a focal length of 
35 cm. If the nearest distance of distinct vision for the per- 
son be 87.5 cm., at what distance will he see best by the aid of 
the spectacles? Ans. 25 cm. 

ELECTRICITY. 

1. Six leyden jars are charged by cascade. If the poten- 
tial of the machine be 6,000 volts, what will be the potential 
of the inside coating of the first jar when it is disconnected 
from the machine and the second jar, and its outside coating 
connected with the earth? Ans. 1,000 volts. 

2. The conductivity of a wire is 60. What resistance will 
there be in a wire 100 cm. long and 1 cm. diameter? 

Ans. 2.12 ohms. 

e ^ v 

3. Show that C = 



r+R~Nr +R 

ri 1 



r is the internal resistance of one cell; N, the total number of 
cells; F, the voltage of one cell; «, the number of series; and. R, the 
resistance in the external circuit. 



150 PHYSICAL LABORATORY MANUAL. 

4. If V=I volt, r=I ohm, and 7?=20 ohms, what will be 
the smallest number of cells that will give a current of 1.5 
ampere? How will they be arranged? 

Ans. 180 cells in three series. 

5. If the conditions be the same as in problem 4, what 
will be the smallest number of cells that will give a current of 
1.9 ampere? How will they be arranged? 

Ans. 300 cells in four series. 

6. In measuring the fall of potential over a wire carrying a 
current, the distance between the connections of the galva- 
nometer circuit was 5 cm. The galvanometer showed a cur- 
rent of .01 ampere. If the total resistance in the battery cir- 
cuit was 100 cm. of the wire, and the electromotive force of 
the battery was 4 volts, what was the resistance through the 
galvanometer circuit? Ans. 20 ohms. 

7. The resistance of two coils in parallel is 4 ohms. If the 
resistance of one of the coils be 6.4 ohms, what is the resist- 
ance of the other coil? Ans. 10.67 ohms. 

8. A galvanometer with a shunt having 5 ohms resistance 
is placed in parallel with a resistance of 20 ohms. If .01 of 
the current pass through the galvanometer, what is the resist- 
ance through the galvanometer? Ans. 396 ohms. 

9. 800 incandescent lights are arranged in parallel. The 
resistance of each light is 180 ohms. What current flows 
through the external circuit when the electromotive force is 
100 volts? , Ins. 444.4 amperes. 

10. If the shunt for the field magnets of the dynamo, prob- 
lem 9, have a resistance of 10 ohms, what current passes 
through the armature? Ans. 454.4 amperes. 



PHYSICAL LABORATORY MANUAL. 153 



TABLES. 



The sines and tangents are found directly from the table. 
The cosine of any angle is found by subtracting the angle 
from 90 and taking the sine of the remainder. The cotan- 
gent is found by subtracting the angle from 90 and taking 
the tangent of the remainder. 



NATURAL SINES AND TANGENTS. 





0' 


20' 


40' 


Angl e. 




























SINK. 


TANG. 


SINE. 


Tang. 


SINE. 


TANG. 





.0000 00 


.0000 


.0058 18 


.0058 2 


.0116 35 


.0116 4 


1 


.0174 52 


.0174 6 


.0232 7 


.0232 8 


.0290 8 


.02910 


2 


.0349 


.0349 2 


.04071 


.0407 5 


.0465 3 


.0465 8 


3 


.0523 4 


.0524 1 


.05814 


.0582 4 


.0639 5 


.0640 8 


4 


.0697 6 


.0699 3 


.0755 6 


.0757 8 


.0813 6 


.0816 3 


5 


.0871 6 


.0874 9 


.0929 5 


.0933 5 


.0987 4 


.0992 3 


6 


.1045 3 


.10510 


.1103 1 


.1109 9 


.1160 9 


.1168 8 


7 


.1218 7 


.1227 8 


.1276 4 


.1286 9 


.1334 


.1346 


8 


.1392 


.1405 


.1449 


.1465 


.1507 


.1524 


9 


.1564 


.1584 


.1622 


.1644 


.1679 


.1703 


10 


.1736 


.1763 


.1794 


.1823 


.1851 


.1883 


11 


.1908 


.1944 


.1965 


.2004 


.2022 


.2065 


12 


.2079 


.2126 


.2136 


.2186 


.2193 


.2247 


13 


.2250 


.2309 


.2306 


.2370 


.2363 


.2432 


14 


.2419 


.2493 


.2476 


.2555 


.2532 


.2617 


15 


.2588 


.2679 


.2644 


.2742 


.2700 


.2805 


16 


.2756 


.2867 


.2812 


.2931 


.2868 


.2994 


17 


.2924 


.3057 


.2979 


.3121 


.3035 


.3185 


18 


.3090 


.3249 


.3145 


.3314 


.3201 


.3378 


19 


.3256 


.3443 


.3311 


.3508 


.3365 


.3574 


20 


.3420 


.3640 


.3475 


.3706 


.3529 


.3772 


21 


.3584 


.3839 


.3638 


.3906 


.3692 


.3973 


22 


.3746 


.4040 


.3800 


.4108 


.3854 


.4176 


23 


.3907 


.4245 


.3961 


.4314 


.4014 


.4383 


24 


.4067 


.4452 


.4120 


.4522 


.4173 


.4592 


25 


.4226 


.4663 


.4279 


.4734 


.4331 


.4806 


26 


.4384 


.4877 


.4436 


.4950 


.4488 


.5022 


27 


.4540 


.5095 


.4592 


.5169 


.4643 


.5243 


28 


.4695 


.5317 


.4746 


.5392 


.4797 


.5467 


29 


.4848 


.5543 


.4899 


.5619 


.4950 


.5696 


30 


.5000 


.5774 


.5050 


.5851 


5100 


.5930 


31 


.5150 


.6009 


.5200 


.6088 


.5250 


.6168 


32 


.5299 


.6249 


.5348 


.6330 


.5398 


.6412 


33 


.5446 


.6494 


.5495 


.6577 


.5544 


.6661 


34 


.5592 


.6745 


.5640 


.6830 


.5688 


.6916 


35 


.5736 


.7002 


.5783 


.7089 


.5831 


.7177 


36 


.5878 


.7265 


.5925 


.7355 


.5972 


.7445 


37 


.6018 


.7536 


.6065 


.7627 


.6111 


.7720 


38 


.6157 


.7813 


.6202 


.7907 


.6248 


.8002 


39 


.6293 


.8098 


.6338 


.8195 


.6383 


.8292 


40 


.6428 


.8391 


.6472 


.8491 


.6517 


[8591 


41 


.6561 


.8693 


.6604 


.8796 


.6648 


.8899 


42 


.6691 


.9004 


.6734 


.9110 


.6777 


.9217 


43 


.6820 


.9325 


.6862 


.9435 


.6905 


.9545 


44 


.6947 


.9657 


.6988 


.9770 


.7030 


.9888 



NATURAL SINES AND TANGENTS. 



1ST 





0' 


20' 


40' 


Angle, 




























SINE. 


TANG. 


SINE. 


TANG. 


SINE. 


TANG. 


45 


.7071 


1.0000 


.7112 


1.0117 


.7153 


1.0235 


46 


.7193 


1.0355 


.7234 


1.0477 


.7274 


1.0599 


47 


.7314 


1.0724 


.7353 


1 0850 


.7392 


1.0977 


48 


.7431 


1.1106 


.7470 


1.1237 


.7509 


1.1369 


49 


.7547 


1.1504 


.7585 


1.1640 


.7623 


1.1778 


SO 


.7660 


1.1918 


.7698 


1.2059 


.7735 


1.2203 


51 


.7771 


1.2349 


.7808 


1.2497 


.7844 


1.2647 


52 


.7880 


1.2799 


.7916 


1.2954 


.7951 


1.3111 


S3 


.7986 


1.3270 


.8021 


1.3432 


.8056 


1.3597 


54 


.8090 


1.3764 


.8124 


1.3934 


.8158 


1.4106 


55 


.8192 


1.4281 


.8225 


1.4460 


.8258 


1.4641 


56 


.8290 


1.4826 


.8323 


1.5013 


.8355 


1.5204 


57 


.8387 


1.5399 


.8418 


1.5597 


.8450 


1.5798 


58 


.8480 


1.6003 


.8511 


1.6212 


.8542 


1.6426 


59 


8572 


1.6643 


.8601 


1.6864 


.8631 


1.7090 


60 


.8660 


1.7321 


.8689 


1.7556 


.8718 


1.7796 


61 


.8746 


1.8040 


.8774 


1.8291 


.8802 


1.8546 


62 


.8829 


1.8807 


.8857 


1.9074 


.8884 


1.9347 


63 


.8910 


1.9626 


.8936 


1.9912 


.8962 


2.0204 


64 


.8988 


2.0503 


.9013 


2.0809 


.9038 


2.1123 


65 


.9063 


2.1445 


.9088 


2.1775 


.9112 


2.2113 


66 


.9135 


2.2460 


.9159 


2.2817 


.9182 


2.3183 


67 


.9205 


2.3559 


.9228 


2.3945 


.9250 


2.4342 


68 


.9272 


2.4751 


.9293 


2.5172 


.9315 


2.5605 


69 


.9336 


'2.6051 


.9356 


2.6511 


.9377 


2.6985 


70 


.9397 


2.7475 


.9417 


2.7980 


.9436 


2.8502 


71 


.9455 


2.9042 


.9474 


2.9600 


.9492 


3.0178 


72 


.9511 


3.0777 


.9528 


3.1397 


.9546 


3.2041 


73 


.9563 


3.2709 


.9580 


3.3402 


.9596 


3.4124 


74 


.9613 


3.4874 


.9628 


3.5656 


.9644 


3.6470 


75 


.9659 


3.7321 


.9674 


3.8208 


.9689 


3.9136 


76 


.9703 


4.0108 


.9717 


4.1126 


.9730 


4.2193 


77 


.9744 


4.3315 


.9757 


4.4494 


.9769 


4.5736 


78 


.9781 


4.7046 


.9793 


4.8430 


.9805 


4.9894 


79 


.9816 


5.1446 


.9827 


5.3093 


.9838 


5.4845 


80 


.9848 


5.6713 


.9858 


5.8708 


.9868 


6.0844 


81 


.9877 


6.3138 


.9886 


6.5606 


.9894 


6.8269 


82 


.9903 


7.1154 


.9911 


7.4287 


.9918 


7.7704 


83 


.9925 


8.1443 


.9932 


8.5555 


.9939 


9.0098 


84 


.9945 


9.5144 


.9951 


10.0780 


.9957 


10.7119 


85 


.9962 


11.4301 


.9967 


12.2505 


.9971 


13.1969 


86 


.9976 


14.3007 


.9980 


15.6048 j 


.9983 


17.1693 


87 


.9986 


19.0811 


.9989 


21.4704 


.9992 


24.5418 


88 


.9994 


28.6363 


.9996 


34.3678 


.9997 


42.9641 


89 


.9998 


57.2900 


.9999 


85.9398 ' 


1.0000 


171.8854 



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